-
-
Notifications
You must be signed in to change notification settings - Fork 11
/
Copy pathnumpy.random.Generator.standard_cauchy.html
797 lines (593 loc) · 39.1 KB
/
numpy.random.Generator.standard_cauchy.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
<!DOCTYPE html>
<html lang="en" data-content_root="../../../" data-theme="light">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
<title>numpy.random.Generator.standard_cauchy — NumPy v2.3.dev0 Manual</title>
<script data-cfasync="false">
document.documentElement.dataset.mode = localStorage.getItem("mode") || "light";
document.documentElement.dataset.theme = localStorage.getItem("theme") || "light";
</script>
<!--
this give us a css class that will be invisible only if js is disabled
-->
<noscript>
<style>
.pst-js-only { display: none !important; }
</style>
</noscript>
<!-- Loaded before other Sphinx assets -->
<link href="../../../_static/styles/theme.css?digest=8878045cc6db502f8baf" rel="stylesheet" />
<link href="../../../_static/styles/pydata-sphinx-theme.css?digest=8878045cc6db502f8baf" rel="stylesheet" />
<link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=8f2a1f02" />
<link rel="stylesheet" type="text/css" href="../../../_static/graphviz.css?v=eafc0fe6" />
<link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
<link rel="stylesheet" type="text/css" href="../../../_static/copybutton.css?v=76b2166b" />
<link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=Vibur" />
<link rel="stylesheet" type="text/css" href="../../../_static/jupyterlite_sphinx.css?v=2c9f8f05" />
<link rel="stylesheet" type="text/css" href="../../../_static/sphinx-design.min.css?v=95c83b7e" />
<link rel="stylesheet" type="text/css" href="../../../_static/numpy.css?v=a1b581f7" />
<!-- So that users can add custom icons -->
<script src="../../../_static/scripts/fontawesome.js?digest=8878045cc6db502f8baf"></script>
<!-- Pre-loaded scripts that we'll load fully later -->
<link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=8878045cc6db502f8baf" />
<link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=8878045cc6db502f8baf" />
<script src="../../../_static/documentation_options.js?v=81ea5b28"></script>
<script src="../../../_static/doctools.js?v=888ff710"></script>
<script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
<script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
<script src="../../../_static/copybutton.js?v=30646c52"></script>
<script src="../../../_static/jupyterlite_sphinx.js?v=96e329c5"></script>
<script src="../../../_static/design-tabs.js?v=f930bc37"></script>
<script async="async" src="../../../_static/scipy-mathjax/MathJax.js?config=scipy-mathjax"></script>
<script>DOCUMENTATION_OPTIONS.pagename = 'reference/random/generated/numpy.random.Generator.standard_cauchy';</script>
<script>
DOCUMENTATION_OPTIONS.theme_version = '0.16.1';
DOCUMENTATION_OPTIONS.theme_switcher_json_url = 'https://numpy.org/doc/_static/versions.json';
DOCUMENTATION_OPTIONS.theme_switcher_version_match = 'devdocs';
DOCUMENTATION_OPTIONS.show_version_warning_banner =
true;
</script>
<link rel="icon" href="../../../_static/favicon.ico"/>
<link rel="index" title="Index" href="../../../genindex.html" />
<link rel="search" title="Search" href="../../../search.html" />
<link rel="next" title="numpy.random.Generator.standard_exponential" href="numpy.random.Generator.standard_exponential.html" />
<link rel="prev" title="numpy.random.Generator.rayleigh" href="numpy.random.Generator.rayleigh.html" />
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<meta name="docsearch:language" content="en"/>
<meta name="docsearch:version" content="2.3.dev0" />
<meta name="docbuild:last-update" content="Apr 22, 2025"/>
</head>
<body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="light">
<div id="pst-skip-link" class="skip-link d-print-none"><a href="#main-content">Skip to main content</a></div>
<div id="pst-scroll-pixel-helper"></div>
<button type="button" class="btn rounded-pill" id="pst-back-to-top">
<i class="fa-solid fa-arrow-up"></i>Back to top</button>
<dialog id="pst-search-dialog">
<form class="bd-search d-flex align-items-center"
action="../../../search.html"
method="get">
<i class="fa-solid fa-magnifying-glass"></i>
<input type="search"
class="form-control"
name="q"
placeholder="Search the docs ..."
aria-label="Search the docs ..."
autocomplete="off"
autocorrect="off"
autocapitalize="off"
spellcheck="false"/>
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form>
</dialog>
<div class="pst-async-banner-revealer d-none">
<aside id="bd-header-version-warning" class="d-none d-print-none" aria-label="Version warning"></aside>
</div>
<header class="bd-header navbar navbar-expand-lg bd-navbar d-print-none">
<div class="bd-header__inner bd-page-width">
<button class="pst-navbar-icon sidebar-toggle primary-toggle" aria-label="Site navigation">
<span class="fa-solid fa-bars"></span>
</button>
<div class="col-lg-3 navbar-header-items__start">
<div class="navbar-item">
<a class="navbar-brand logo" href="../../../index.html">
<img src="../../../_static/numpylogo.svg" class="logo__image only-light" alt="NumPy v2.3.dev0 Manual - Home"/>
<img src="../../../_static/numpylogo_dark.svg" class="logo__image only-dark pst-js-only" alt="NumPy v2.3.dev0 Manual - Home"/>
</a></div>
</div>
<div class="col-lg-9 navbar-header-items">
<div class="me-auto navbar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../../user/index.html">
User Guide
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../../index.html">
API reference
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../../building/index.html">
Building from source
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../../dev/index.html">
Development
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../../release.html">
Release notes
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://numpy.org/numpy-tutorials/">
Learn
</a>
</li>
<li class="nav-item dropdown">
<button class="btn dropdown-toggle nav-item" type="button"
data-bs-toggle="dropdown" aria-expanded="false"
aria-controls="pst-nav-more-links">
More
</button>
<ul id="pst-nav-more-links" class="dropdown-menu">
<li class=" ">
<a class="nav-link dropdown-item nav-external" href="https://numpy.org/neps">
NEPs
</a>
</li>
</ul>
</li>
</ul>
</nav></div>
</div>
<div class="navbar-header-items__end">
<div class="navbar-item">
<button class="btn btn-sm pst-navbar-icon search-button search-button__button pst-js-only" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass fa-lg"></i>
</button></div>
<div class="navbar-item">
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button pst-js-only" aria-label="Color mode" data-bs-title="Color mode" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light" title="Light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark" title="Dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto" title="System Settings"></i>
</button></div>
<div class="navbar-item">
<div class="version-switcher__container dropdown pst-js-only">
<button id="pst-version-switcher-button-2"
type="button"
class="version-switcher__button btn btn-sm dropdown-toggle"
data-bs-toggle="dropdown"
aria-haspopup="listbox"
aria-controls="pst-version-switcher-list-2"
aria-label="Version switcher list"
>
Choose version <!-- this text may get changed later by javascript -->
<span class="caret"></span>
</button>
<div id="pst-version-switcher-list-2"
class="version-switcher__menu dropdown-menu list-group-flush py-0"
role="listbox" aria-labelledby="pst-version-switcher-button-2">
<!-- dropdown will be populated by javascript on page load -->
</div>
</div></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://github.com/numpy/numpy" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-github fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitHub</span></a>
</li>
</ul></div>
</div>
</div>
<button class="pst-navbar-icon sidebar-toggle secondary-toggle" aria-label="On this page">
<span class="fa-solid fa-outdent"></span>
</button>
</div>
</header>
<div class="bd-container">
<div class="bd-container__inner bd-page-width">
<dialog id="pst-primary-sidebar-modal"></dialog>
<div id="pst-primary-sidebar" class="bd-sidebar-primary bd-sidebar">
<div class="sidebar-header-items sidebar-primary__section">
<div class="sidebar-header-items__center">
<div class="navbar-item">
<nav>
<ul class="bd-navbar-elements navbar-nav">
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../../user/index.html">
User Guide
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../../index.html">
API reference
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../../building/index.html">
Building from source
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../../dev/index.html">
Development
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-internal" href="../../../release.html">
Release notes
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://numpy.org/numpy-tutorials/">
Learn
</a>
</li>
<li class="nav-item ">
<a class="nav-link nav-external" href="https://numpy.org/neps">
NEPs
</a>
</li>
</ul>
</nav></div>
</div>
<div class="sidebar-header-items__end">
<div class="navbar-item">
<button class="btn btn-sm pst-navbar-icon search-button search-button__button pst-js-only" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass fa-lg"></i>
</button></div>
<div class="navbar-item">
<button class="btn btn-sm nav-link pst-navbar-icon theme-switch-button pst-js-only" aria-label="Color mode" data-bs-title="Color mode" data-bs-placement="bottom" data-bs-toggle="tooltip">
<i class="theme-switch fa-solid fa-sun fa-lg" data-mode="light" title="Light"></i>
<i class="theme-switch fa-solid fa-moon fa-lg" data-mode="dark" title="Dark"></i>
<i class="theme-switch fa-solid fa-circle-half-stroke fa-lg" data-mode="auto" title="System Settings"></i>
</button></div>
<div class="navbar-item">
<div class="version-switcher__container dropdown pst-js-only">
<button id="pst-version-switcher-button-3"
type="button"
class="version-switcher__button btn btn-sm dropdown-toggle"
data-bs-toggle="dropdown"
aria-haspopup="listbox"
aria-controls="pst-version-switcher-list-3"
aria-label="Version switcher list"
>
Choose version <!-- this text may get changed later by javascript -->
<span class="caret"></span>
</button>
<div id="pst-version-switcher-list-3"
class="version-switcher__menu dropdown-menu list-group-flush py-0"
role="listbox" aria-labelledby="pst-version-switcher-button-3">
<!-- dropdown will be populated by javascript on page load -->
</div>
</div></div>
<div class="navbar-item"><ul class="navbar-icon-links"
aria-label="Icon Links">
<li class="nav-item">
<a href="https://github.com/numpy/numpy" title="GitHub" class="nav-link pst-navbar-icon" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><i class="fa-brands fa-square-github fa-lg" aria-hidden="true"></i>
<span class="sr-only">GitHub</span></a>
</li>
</ul></div>
</div>
</div>
<div class="sidebar-primary-items__start sidebar-primary__section">
<div class="sidebar-primary-item">
<nav class="bd-docs-nav bd-links"
aria-label="Section Navigation">
<p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
<div class="bd-toc-item navbar-nav"><ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../../module_structure.html">NumPy’s module structure</a></li>
</ul>
<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../../arrays.html">Array objects</a></li>
</ul>
<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../../ufuncs.html">Universal functions (<code class="xref py py-class docutils literal notranslate"><span class="pre">ufunc</span></code>)</a></li>
</ul>
<ul class="current nav bd-sidenav">
<li class="toctree-l1 current active has-children"><a class="reference internal" href="../../routines.html">Routines and objects by topic</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="../../constants.html">Constants</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.array-creation.html">Array creation routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.array-manipulation.html">Array manipulation routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.bitwise.html">Bit-wise operations</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.strings.html">String functionality</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.datetime.html">Datetime support functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.dtype.html">Data type routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.emath.html">Mathematical functions with automatic domain</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.err.html">Floating point error handling</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.exceptions.html">Exceptions and Warnings</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.fft.html">Discrete Fourier Transform</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.functional.html">Functional programming</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.io.html">Input and output</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.indexing.html">Indexing routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.linalg.html">Linear algebra</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.logic.html">Logic functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.ma.html">Masked array operations</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.math.html">Mathematical functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.other.html">Miscellaneous routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.polynomials.html">Polynomials</a></li>
<li class="toctree-l2 current active has-children"><a class="reference internal" href="../index.html">Random sampling</a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l3 current active has-children"><a class="reference internal" href="../generator.html">Random <code class="docutils literal notranslate"><span class="pre">Generator</span></code></a><details open="open"><summary><span class="toctree-toggle" role="presentation"><i class="fa-solid fa-chevron-down"></i></span></summary><ul class="current">
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.bit_generator.html">numpy.random.Generator.bit_generator</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.spawn.html">numpy.random.Generator.spawn</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.integers.html">numpy.random.Generator.integers</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.random.html">numpy.random.Generator.random</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.choice.html">numpy.random.Generator.choice</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.bytes.html">numpy.random.Generator.bytes</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.shuffle.html">numpy.random.Generator.shuffle</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.permutation.html">numpy.random.Generator.permutation</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.permuted.html">numpy.random.Generator.permuted</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.beta.html">numpy.random.Generator.beta</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.binomial.html">numpy.random.Generator.binomial</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.chisquare.html">numpy.random.Generator.chisquare</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.dirichlet.html">numpy.random.Generator.dirichlet</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.exponential.html">numpy.random.Generator.exponential</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.f.html">numpy.random.Generator.f</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.gamma.html">numpy.random.Generator.gamma</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.geometric.html">numpy.random.Generator.geometric</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.gumbel.html">numpy.random.Generator.gumbel</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.hypergeometric.html">numpy.random.Generator.hypergeometric</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.laplace.html">numpy.random.Generator.laplace</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.logistic.html">numpy.random.Generator.logistic</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.lognormal.html">numpy.random.Generator.lognormal</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.logseries.html">numpy.random.Generator.logseries</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.multinomial.html">numpy.random.Generator.multinomial</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.multivariate_hypergeometric.html">numpy.random.Generator.multivariate_hypergeometric</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.multivariate_normal.html">numpy.random.Generator.multivariate_normal</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.negative_binomial.html">numpy.random.Generator.negative_binomial</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.noncentral_chisquare.html">numpy.random.Generator.noncentral_chisquare</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.noncentral_f.html">numpy.random.Generator.noncentral_f</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.normal.html">numpy.random.Generator.normal</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.pareto.html">numpy.random.Generator.pareto</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.poisson.html">numpy.random.Generator.poisson</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.power.html">numpy.random.Generator.power</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.rayleigh.html">numpy.random.Generator.rayleigh</a></li>
<li class="toctree-l4 current active"><a class="current reference internal" href="#">numpy.random.Generator.standard_cauchy</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.standard_exponential.html">numpy.random.Generator.standard_exponential</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.standard_gamma.html">numpy.random.Generator.standard_gamma</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.standard_normal.html">numpy.random.Generator.standard_normal</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.standard_t.html">numpy.random.Generator.standard_t</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.triangular.html">numpy.random.Generator.triangular</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.uniform.html">numpy.random.Generator.uniform</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.vonmises.html">numpy.random.Generator.vonmises</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.wald.html">numpy.random.Generator.wald</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.weibull.html">numpy.random.Generator.weibull</a></li>
<li class="toctree-l4"><a class="reference internal" href="numpy.random.Generator.zipf.html">numpy.random.Generator.zipf</a></li>
</ul>
</details></li>
<li class="toctree-l3"><a class="reference internal" href="../legacy.html">Legacy Generator (RandomState)</a></li>
<li class="toctree-l3"><a class="reference internal" href="../bit_generators/index.html">Bit generators</a></li>
<li class="toctree-l3"><a class="reference internal" href="../upgrading-pcg64.html">Upgrading PCG64 with PCG64DXSM</a></li>
<li class="toctree-l3"><a class="reference internal" href="../compatibility.html">Compatibility policy</a></li>
<li class="toctree-l3"><a class="reference internal" href="../parallel.html">Parallel Applications</a></li>
<li class="toctree-l3"><a class="reference internal" href="../multithreading.html">Multithreaded Generation</a></li>
<li class="toctree-l3"><a class="reference internal" href="../new-or-different.html">What’s new or different</a></li>
<li class="toctree-l3"><a class="reference internal" href="../performance.html">Comparing Performance</a></li>
<li class="toctree-l3"><a class="reference internal" href="../c-api.html">C API for random</a></li>
<li class="toctree-l3"><a class="reference internal" href="../extending.html">Examples of using Numba, Cython, CFFI</a></li>
</ul>
</details></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.set.html">Set routines</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.sort.html">Sorting, searching, and counting</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.statistics.html">Statistics</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.testing.html">Test support</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../routines.window.html">Window functions</a></li>
</ul>
</details></li>
</ul>
<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../../typing.html">Typing (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.typing</span></code>)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../distutils.html">Packaging</a></li>
</ul>
<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../../c-api/index.html">NumPy C-API</a></li>
</ul>
<ul class="nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../../array_api.html">Array API standard compatibility</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../simd/index.html">CPU/SIMD optimizations</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../thread_safety.html">Thread Safety</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../global_state.html">Global Configuration Options</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../security.html">NumPy security</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../distutils_status_migration.html">Status of <code class="docutils literal notranslate"><span class="pre">numpy.distutils</span></code> and migration advice</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../distutils_guide.html"><code class="docutils literal notranslate"><span class="pre">numpy.distutils</span></code> user guide</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../swig.html">NumPy and SWIG</a></li>
</ul>
</div>
</nav></div>
</div>
<div class="sidebar-primary-items__end sidebar-primary__section">
<div class="sidebar-primary-item">
<div id="ethical-ad-placement"
class="flat"
data-ea-publisher="readthedocs"
data-ea-type="readthedocs-sidebar"
data-ea-manual="true">
</div></div>
</div>
</div>
<main id="main-content" class="bd-main" role="main">
<div class="bd-content">
<div class="bd-article-container">
<div class="bd-header-article d-print-none">
<div class="header-article-items header-article__inner">
<div class="header-article-items__start">
<div class="header-article-item">
<nav aria-label="Breadcrumb" class="d-print-none">
<ul class="bd-breadcrumbs">
<li class="breadcrumb-item breadcrumb-home">
<a href="../../../index.html" class="nav-link" aria-label="Home">
<i class="fa-solid fa-home"></i>
</a>
</li>
<li class="breadcrumb-item"><a href="../../index.html" class="nav-link">NumPy reference</a></li>
<li class="breadcrumb-item"><a href="../../module_structure.html" class="nav-link">NumPy’s module structure</a></li>
<li class="breadcrumb-item"><a href="../index.html" class="nav-link">Random sampling</a></li>
<li class="breadcrumb-item"><a href="../generator.html" class="nav-link">Random <code class="docutils literal notranslate"><span class="pre">Generator</span></code></a></li>
<li class="breadcrumb-item active" aria-current="page"><span class="ellipsis">numpy.random.Generator.standard_cauchy</span></li>
</ul>
</nav>
</div>
</div>
</div>
</div>
<div id="searchbox"></div>
<article class="bd-article">
<section id="numpy-random-generator-standard-cauchy">
<h1>numpy.random.Generator.standard_cauchy<a class="headerlink" href="#numpy-random-generator-standard-cauchy" title="Link to this heading">#</a></h1>
<p>method</p>
<dl class="py method">
<dt class="sig sig-object py" id="numpy.random.Generator.standard_cauchy">
<span class="sig-prename descclassname"><span class="pre">random.Generator.</span></span><span class="sig-name descname"><span class="pre">standard_cauchy</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.Generator.standard_cauchy" title="Link to this definition">#</a></dt>
<dd><p>Draw samples from a standard Cauchy distribution with mode = 0.</p>
<p>Also known as the Lorentz distribution.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape. If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn. Default is None, in which case a
single value is returned.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>samples</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>The drawn samples.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The probability density function for the full Cauchy distribution is</p>
<div class="math notranslate nohighlight">
\[P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+
(\frac{x-x_0}{\gamma})^2 \bigr] }\]</div>
<p>and the Standard Cauchy distribution just sets <span class="math notranslate nohighlight">\(x_0=0\)</span> and
<span class="math notranslate nohighlight">\(\gamma=1\)</span></p>
<p>The Cauchy distribution arises in the solution to the driven harmonic
oscillator problem, and also describes spectral line broadening. It
also describes the distribution of values at which a line tilted at
a random angle will cut the x axis.</p>
<p>When studying hypothesis tests that assume normality, seeing how the
tests perform on data from a Cauchy distribution is a good indicator of
their sensitivity to a heavy-tailed distribution, since the Cauchy looks
very much like a Gaussian distribution, but with heavier tails.</p>
<p class="rubric">References</p>
<div role="list" class="citation-list">
<div class="citation" id="redb98c78ab31-1" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></span>
<p>NIST/SEMATECH e-Handbook of Statistical Methods, “Cauchy
Distribution”,
<a class="reference external" href="https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm">https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm</a></p>
</div>
<div class="citation" id="redb98c78ab31-2" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>2<span class="fn-bracket">]</span></span>
<p>Weisstein, Eric W. “Cauchy Distribution.” From MathWorld–A
Wolfram Web Resource.
<a class="reference external" href="https://mathworld.wolfram.com/CauchyDistribution.html">https://mathworld.wolfram.com/CauchyDistribution.html</a></p>
</div>
<div class="citation" id="redb98c78ab31-3" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span>3<span class="fn-bracket">]</span></span>
<p>Wikipedia, “Cauchy distribution”
<a class="reference external" href="https://en.wikipedia.org/wiki/Cauchy_distribution">https://en.wikipedia.org/wiki/Cauchy_distribution</a></p>
</div>
</div>
<p class="rubric">Examples</p>
<div class="try_examples_outer_container docutils container" id="2e5e9cd8-9f7a-40b6-8102-795b7510e328">
<div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesShowIframe('2e5e9cd8-9f7a-40b6-8102-795b7510e328','95e5dabe-c559-4b80-851b-7208cf8ad265','4313a95d-59b1-428a-b926-8d119c17ad49','../../../lite/tree/../notebooks/index.html?path=86286885_4774_42f0_a725_3125e93c77fd.ipynb','None')">Try it in your browser!</button></div><div class="try_examples_content docutils container">
<p>Draw samples and plot the distribution:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<span class="gp">>>> </span><span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">()</span>
<span class="gp">>>> </span><span class="n">s</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">standard_cauchy</span><span class="p">(</span><span class="mi">1000000</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">s</span> <span class="o">=</span> <span class="n">s</span><span class="p">[(</span><span class="n">s</span><span class="o">>-</span><span class="mi">25</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">s</span><span class="o"><</span><span class="mi">25</span><span class="p">)]</span> <span class="c1"># truncate distribution so it plots well</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<figure class="align-default">
<img alt="../../../_images/numpy-random-Generator-standard_cauchy-1.png" class="plot-directive" src="../../../_images/numpy-random-Generator-standard_cauchy-1.png" />
</figure>
</div>
</div>
<div id="4313a95d-59b1-428a-b926-8d119c17ad49" class="try_examples_outer_iframe hidden"><div class="try_examples_button_container"><button class="try_examples_button" onclick="window.tryExamplesHideIframe('2e5e9cd8-9f7a-40b6-8102-795b7510e328','4313a95d-59b1-428a-b926-8d119c17ad49')">Go Back</button><button class="try_examples_button" onclick="window.openInNewTab('2e5e9cd8-9f7a-40b6-8102-795b7510e328','4313a95d-59b1-428a-b926-8d119c17ad49')">Open In Tab</button></div><div id="95e5dabe-c559-4b80-851b-7208cf8ad265" class="jupyterlite_sphinx_iframe_container"></div></div><script>document.addEventListener("DOMContentLoaded", function() {window.loadTryExamplesConfig("../../../try_examples.json");});</script></dd></dl>
</section>
</article>
<footer class="prev-next-footer d-print-none">
<div class="prev-next-area">
<a class="left-prev"
href="numpy.random.Generator.rayleigh.html"
title="previous page">
<i class="fa-solid fa-angle-left"></i>
<div class="prev-next-info">
<p class="prev-next-subtitle">previous</p>
<p class="prev-next-title">numpy.random.Generator.rayleigh</p>
</div>
</a>
<a class="right-next"
href="numpy.random.Generator.standard_exponential.html"
title="next page">
<div class="prev-next-info">
<p class="prev-next-subtitle">next</p>
<p class="prev-next-title">numpy.random.Generator.standard_exponential</p>
</div>
<i class="fa-solid fa-angle-right"></i>
</a>
</div>
</footer>
</div>
<dialog id="pst-secondary-sidebar-modal"></dialog>
<div id="pst-secondary-sidebar" class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
<div class="sidebar-secondary-item">
<div
id="pst-page-navigation-heading-2"
class="page-toc tocsection onthispage">
<i class="fa-solid fa-list"></i> On this page
</div>
<nav class="bd-toc-nav page-toc" aria-labelledby="pst-page-navigation-heading-2">
<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#numpy.random.Generator.standard_cauchy"><code class="docutils literal notranslate"><span class="pre">random.Generator.standard_cauchy</span></code></a></li>
</ul>
</nav></div>
</div></div>
</div>
<footer class="bd-footer-content">
</footer>
</main>
</div>
</div>
<!-- Scripts loaded after <body> so the DOM is not blocked -->
<script defer src="../../../_static/scripts/bootstrap.js?digest=8878045cc6db502f8baf"></script>
<script defer src="../../../_static/scripts/pydata-sphinx-theme.js?digest=8878045cc6db502f8baf"></script>
<footer class="bd-footer">
<div class="bd-footer__inner bd-page-width">
<div class="footer-items__start">
<div class="footer-item">
<p class="copyright">
© Copyright 2008-2025, NumPy Developers.
<br/>
</p>
</div>
<div class="footer-item">
<p class="sphinx-version">
Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.6.
<br/>
</p>
</div>
</div>
<div class="footer-items__end">
<div class="footer-item">
<p class="theme-version">
<!-- # L10n: Setting the PST URL as an argument as this does not need to be localized -->
Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.16.1.
</p></div>
</div>
</div>
</footer>
</body>
</html>