Negative binomial distribution

related topics
{math, number, function}
{rate, high, increase}
{build, building, house}
{law, state, case}
{math, energy, light}
{food, make, wine}
{son, year, death}
{mi², represent, 1st}

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of Bernoulli trials before a specified (non-random) number r of failures occurs. For example, if one throws a die repeatedly until the third time “1” appears, then the probability distribution of the number of non-“1”s that had appeared will be negative binomial.

The Pascal distribution (after Blaise Pascal) and Polya distribution (for George Pólya) are special cases of the negative binomial. There is a convention among engineers, climatologists, and others to reserve “negative binomial” in a strict sense or “Pascal” for the case of an integer-valued stopping-time parameter r, and use “Polya” for the real-valued case. The Polya distribution more accurately models occurrences of “contagious” discrete events, like tornado outbreaks, than the Poisson distribution.

Contents

Full article ▸

related documents
Exponential distribution
Miranda (programming language)
Elementary algebra
Ideal (ring theory)
Abel–Ruffini theorem
Unlambda
Natural logarithm
Gödel's completeness theorem
Division (mathematics)
Locally compact space
Trace (linear algebra)
Cauchy–Schwarz inequality
Power series
Chinese remainder theorem
String (computer science)
Isomorphism
Transposition cipher
Brute-force search
Holomorphic function
Rice's theorem
Logical connective
Normed vector space
J (programming language)
Merge sort
Ordinary differential equation
Tychonoff's theorem
Scope (programming)
Objective Caml
Field extension
Key size