DISCRETE
Bernoulli distribution, discrete probability distribution, which takes value 1 with success probability
and value 0 with failure probability
. binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probabilityp.
Such a success/failure experiment is also called a Bernoulli experiment or Bernoulli trial; when n = 1, the Bernoulli distribution is a binomial distribution. The binomial distribution is the basis for the popular binomial testof statistical significance.
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 of failures (denoted r) occurs. For example, if we define a "1" as failure, and all non-"1"s as successes, and we throw a dierepeatedly until the third time “1” appears (r = three failures), then the probability distribution of the number of non-“1”s that had appeared will be negative binomial.
Poisson distribution (pronounced [pwasɔ̃]) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event
The categorical distribution is the generalization of the Bernoulli distribution for a categorical random variable, i.e. for a discrete variable with more than two possible outcomes.
multinomial distribution is a generalization of the binomial distribution. For nindependent trials each of which leads to a success for exactly one of k categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories.
hypergeometric distribution is a discrete probability distribution that describes the probability of
successes in 
draws without replacement from a finite population of size 
containing a maximum of 
successes. This is in contrast to the binomial distribution, which describes the probability of successes in draws with replacement.
geometric distribution is either of two discrete probability distributions:
- The probability distribution of the number of X Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...}
- The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... }
Continuous
normal (or Gaussian) distribution is a continuous probability distribution, defined by the formula
- With a shape parameter k and a scale parameter θ.
- With a shape parameter α = k and an inverse scale parameter β = 1/θ, called a rate parameter.
- With a shape parameter k and a mean parameter μ = k/β.
multivariate normal distribution or multivariate Gaussian distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions
continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values
Pareto distribution, named after the Italian economist Vilfredo Pareto, is a power law probability distribution that is used in description of social, scientific, geophysical, actuarial, and many other types of observable phenomena
Weibull distribution /ˈveɪbʊl/ is a continuous probability distribution. It is named after Waloddi Weibull, who described it in detail in 1951, although it was first identified by Fréchet (1927) and first applied by Rosin & Rammler (1933) to describe a particle size distribution
log-normal distribution is a continuous probability distribution of a random variablewhose logarithm is normally distributed
exponential distribution (a.k.a. negative exponential distribution) is a family of continuous probability distributions. It describes the time between events in a Poisson process, i.e. a process in which events occur continuously and independently at a constant average rate. It is the continuous analogue of the geometric distribution.
gamma distribution is a two-parameter family of continuousprobability distributions. There are three different parameterizations in common use:
In each of these three forms, both parameters are positive real numbers.
The parameterization with k and θ appears to be more common in econometrics and certain other applied fields, where e.g. the gamma distribution is frequently used to model waiting times. For instance, in life testing, the waiting time until death is a random variable that is frequently modeled with a gamma distribution.[1]
The parameterization with α and β is more common in Bayesian statistics, where the gamma distribution is used as a conjugate prior distribution for various types of inverse scale (aka rate) parameters, such as the λ of an exponential distribution or a Poisson distribution – or for that matter, the β of the gamma distribution itself. (The closely related inverse gamma distribution is used as a conjugate prior for scale parameters, such as the variance of a normal distribution.)
If k is an integer, then the distribution represents an Erlang distribution; i.e., the sum of k independentexponentially distributed random variables, each of which has a mean of θ (which is equivalent to a rate parameter of 1/θ).
beta-binomial distribution is a family of discrete probability distributionson a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. It is frequently used in Bayesian statistics, empirical Bayes methods and classical statistics as an overdispersed binomial distribution
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