Types of Distribution

Bernoulli vs. uniform distribution. The number of ways to distribute the brownies (assumed identical) is indeed $\dbinom{22}{2}$, by a standard "Stars and Bars" argument. However, these $\dbinom{22}{2}$ ways are not all equally likely.

Second, a consequence of the beta distribution being an exponential family is that it is the maximum entropy distribution for a set of sufficient statistics. In the beta distribution's case these statistics are $\log(x)$ and $\log(1-x)$ for $x$ in $[0,1]$. That means that if you only keep the average measurement of these sufficient statistics for a set of samples $x_1, \dots, x_n$, the minimum assumption you can make about the distribution of the samples is that it is beta-distributed.

Journal of Statistics Education, Volume 21, Number 1 (2013) 1 Distinguishing Between Binomial, Hypergeometric and Negative Binomial Distributions

The binomial distribution is the basis for the popular binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N.

The box plot (a.k.a. box and whisker diagram) is a standardized way of displaying the distribution of data based on the five number summary: minimum, first quartile, median, third quartile, and maximum.

Uniform distribution (continuous) In probability theory and statistics, the 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.

In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion.

In mathematics, a degenerate distribution is a probability distribution in a space (discrete or continuous) with support only on a space of lower dimension. If the degenerate distribution is univariate (involving only a single random variable) it is a deterministic distribution and takes only a single value.

In this lesson you will learn about the shape of the distribution of data by looking at various graphs and observing symmetry, bell curves and skews.

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This concerns the relationship between the Gamma and Beta distributions as opposed to the Gamma and Beta functions. Let $X \sim \mbox{Gamma}(\alpha, 1)$ and $Y \sim \mbox{Gamma}(\beta, 1)$ where the paramaterization is such that $\alpha$ is the shape parameter.

Geometric Distribution versus Negative Binomial Distribution. The geometric distribution describes the probability of "x trials are made before a success", and the negative binomial distribution describes that of "x trials are made before $r$ successes are obtained", where $r$ is fixed.

Kumaraswamy distribution. In probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval [0,1].

Distributions related to the normal distribution Three important distributions: Chi-square (˜2) distribution. tdistribution. Fdistribution. Before we discuss the ˜2;t, and F distributions here are few important things about the gamma distribution. The gamma distribution is useful in modeling skewed distributions for variables that are not negative.

The Poisson Distribution In the picture above are simultaneously portrayed several Poisson distributions. Where the rate of occurrence of some event, r (in this chart called lambda or l) is small, the range of likely possibilities will lie near the zero line.

The probability mass function for the Skellam distribution for a difference = − between two independent Poisson-distributed random variables with means and is given by: (;,) = {=} = − (+) / () where I k (z) is the modified Bessel function of the first kind.