Moment (mathematics)

In mathematics, a moment is a specific quantitative measure, used in both mechanics and statistics, of the shape of a set of points. If the points represent mass, then the zeroth moment is the total mass, the first moment divided by the total mass is the center of mass, and the second moment is the rotational inertia. If the points represent probability density, then the zeroth moment is the total probability (i.e. one), the first moment is the mean, the second central moment is the variance, the third moment is the skewness, and the fourth moment (with normalization and shift) is the kurtosis. The mathematical concept is closely related to the concept of moment in physics.

For a bounded distribution of mass or probability, the collection of all the moments (of all orders, from 0 to ∞) uniquely determines the distribution.

Significance of the moments

The n-th moment of a real-valued continuous function f(x) of a real variable about a value c is

It is possible to define moments for random variables in a more general fashion than moments for real values—see moments in metric spaces. The moment of a function, without further explanation, usually refers to the above expression with c = 0.

Moment

Moment or Moments may refer to:

Science, engineering, and mathematics

Art and entertainment

Albums

Songs

Other media

Moment (album)

Moment is Japanese J-pop band Speed's greatest hits album following their first album, Starting Over and second album, Rise. Moment was released on December 16, 1998 and contains all the commercially released singles from their first and second albums along with additional tracks. Debuting at number 1 on the Oricon charts and eventually selling 2.32 million copies, Moment is the best-selling album by a female group in Japanese music history.

Track listing

References

Moment (time)

A moment (momentum) was a medieval unit of time. The movement of a shadow on a sundial covered 40 moments in a solar hour. An hour in this case means one twelfth of the period between sunrise and sunset. The length of a solar hour depended on the length of the day, which in turn varied with the season, so the length of a moment in modern seconds was not fixed, but on average, a moment corresponds to 90 seconds: A day was divided into 24 hours (of unequal lengths, twelve hours of the day and the night each), and an hour was divided into four puncta (quarter-hours), ten minuta and 40 momenta.

The unit was used by medieval computists before the introduction of the mechanical clock and the base 60 system in the late 13th century. The unit would not have been used in everyday life. For our medieval counterparts the main marker of the passage of time was the call to prayer at intervals throughout the day.

The earliest reference we have to the moment is from the 8th century writings of the Venerable Bede. Bede describes the system as 1 hour = 4 points = 10 minutes = 15 parts = 40 moments. Bede was referenced four centuries later by Bartholomeus Anglicus in his early encyclopedia De Proprietatibus Rerum (On the Properties of Things). Centuries after Bede's description, the moment was further divided into 60 ostents, although no such divisions could ever have been used in observation with equipment in use at the time.

Statistics

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all persons living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.

When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.

Denver Dalley

Denver Collin Dalley is an American singer-songwriter based in Omaha, Nebraska. He is best known for his collaboration with Bright Eyes frontman Conor Oberst in Desaparecidos, and has been involved in various other musical projects, including Statistics, Intramural, and Two of Cups.

Career

Desaparecidos

Dalley collaborated with childhood friend Conor Oberst as main songwriter of the politically charged indie rock band Desaparecidos. The band released Read Music/Speak Spanish on Omaha-based Saddle Creek Records before going on hiatus in 2003. They reunited in 2010, performing at the Concert for Equality in Omaha on July 31, and again on July 31, 2012 at Omaha's Maha Music Festival.

Statistics

In 2003, following the temporary caesura of Desaparecidos, Dalley formed Statistics, an electronic-tinged solo project, and signed onto the Jade Tree Records label. After releasing a self-titled extended play in 2003 and two studio albums titled Leave Your Name and Often Lie in 2004 and 2005, respectively, Dalley chose to focus on other projects, effectively putting Statistics on hiatus. However, in 2013, eight years after Often Lie, Dalley released a new studio album titled Peninsula on Afternoon Records, featuring a collaboration with Minnesota-based singer-songwriter Sean Tillman (a.k.a. Har Mar Superstar). Dalley hopes to create visuals in the form of music videos for songs in Peninsula, something that he has never done in his prior musical ventures.

Statistics (disambiguation)

Statistics is a mathematical science pertaining to the collection, analysis, interpretation, and presentation of data.

Statistic may also refer to: