Date: Fri, 7 Oct 2022 10:16:27 +0000 (UTC) Message-ID: <98958711.8199.1665137787304@localhost> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_8198_1082347034.1665137787304" ------=_Part_8198_1082347034.1665137787304 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Discrete distributions

# Discrete distributions

The table below gives an overview of the various discrete distributions = described in ModelAssist, so that you can most easily focus on which ones m= ight be most appropriate for your modeling needs. Follow the links for an i= n-depth explanation of each. We have used the most common name for each dis= tribution.

 Distributions Example use Bernoulli Returns a 1 with probability p and a zero oth= erwise. Binomial Shows the number of successes from n independ= ent trials where there is a probability p of success in each trial. Beta-binomial A binomial variable where p is also a Beta-di= stributed random variable. Discrete Describes a variable that can take one of sev= eral explicit discrete values with different probabilities. D= iscrete uniform Describes a variable that can take one of sev= eral explicit discrete values with equal probabilities. Geometric Models the total number of trials that will o= ccur before a success, given that p is the probability of succeeding. Hypergeometric Models the number of items of a particular ty= pe there will be in a sample of size n where that sample is drawn from a po= pulation of size M of which D are also of that particular type. <= span style=3D"color: rgb(0,0,255);">Integer uniform Describe a variable that can take one of seve= ral sequential discrete values. Inverse Hypergeometric Models the total number of trials one would h= ave to do before achieving the s-th success in a hypergeometric sampling. Logarithmic A one parameter, positive distribution someti= mes used to model frequency of insurance claims. Also used for insect speci= es abundance Multinomi= al An extension of the Binomial distribution whe= re more than two different states of a trial exist. Multivariate Hypergeometric An extension of the Hypergeometric distributi= on where more than two sub-populations of interest exist. Negative Binomial Models the total number of trials there will = be before s successes are achieved where there is a probability p of succes= s with each trial. Also models a Poisson random variable whose mean is a (G= amma) random variable. Poisson Models the number of occurrences of an event = in a time t when the time between successive events follows a Poisson proce= ss

A discrete distribution may take one of a set of identifiable values, ea= ch of which has a calculable probability of occurrence. Discrete distributi= ons are used to model parameters like the number of bridges a roading schem= e may need, the number of key personnel to be employed or the number of cus= tomers that will arrive at a service station in an hour. Clearly, variables= such as these can only take specific values: one cannot build half a bridg= e, employ 2.7 people or serve 13.6 customers.

The vertical scale of a relative frequency plot of a discrete distributi= on is the actual probability of occurrence, sometimes called the p= robability mass. These probabilities must sum to one.

The most common examples of discrete distributions are: Binomial= GeometricHypergeometricNegative Binomial,&n= bsp;Poisson and, of course, the ge= neralized Discrete distribut= ion. The links below discuss different ways of categorizing distributions t= hat may help in your selection of the most appropriate distribution to use:=

Bounded and = unbounded distributions

Para= metric and non-parametric distributions

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