In statistics, probability distribution is used to identify either the probability of the value falling within a particular interval (variable is continuous) or the probability of every value of a random variable (with discrete variable). It describes the range of possible values which can be attained by a random variable. Probability distribution has several variations depending on its basic qualities and principles. Usually we can classify a probability distribution on the base of:

Related to real-valued quantities that grow linearly:

Related to positive real-valued quantities that grow exponentially

Related to real-valued quantities that are assumed to be uniformly distributed

Related to Bernoulli trials

Basic distributions

Related to sampling schemes over a finite population

Related to categorical outcomes

Related to events in a Poisson process

Useful for hypothesis testing related to normally-distributed outcomes

Useful as conjugate prior distributions in Bayesian inference

Besides this, probability distribution has various forms including Bernoulli, Beta, Beta-binomial, Binomial, Boltzmann, Bose–Einstein, Cantor, phase-type, truncated and the mixture, categorical, Cauchy, Chernoff’s, Chi-square, Continuous uniform, Conway–Maxwell–Poisson, Degenerate, Degenerate, Dirac delta function, Discrete uniform, Exponential, Exponential, Fermi–Dirac, Fisher’s non-central hyper geometric, Fisher’s z-distribution, Gamma, Generalized extreme, logistic and normal value, Geometric, Gibbs, Hotelling’s T-square, Hyperbolic, Hyper-geometric, Inverse Gaussian distribution, Inverse-gamma, Irwin-Hall, Kent, Kumaraswamy, Laplace, Lévy, Logarithmic (series), Logistic, Logitnormal, Maxwell–Boltzmann, Multinomial, Negative binomial, Non-central chi, Normal exponential-gamma, Parabolic fractal, Pareto, Pearson Type III distribution, Poisson binomial, Rademacher, Raised cosine, Rectangular, Rice, Scale-inverse-chi-square and forms of chi, Skellam, Skellam, Triangular, Von Mises-Fisher, Wallenius’ noncentral hypergeometric, Weibull or Rosin Rammler, Wishart and inverse-Wishart, Yule–Simon, Zeta and Zipf’s law.