MathType
Wiris Quizzes
Learning Lemur
CalcMe
MathPlayer
Store FAQ
VPAT for the electronic documentation
MathFlow
BF FAQ
Miscellaneous

Probability distributions

Reading time: 1min

It is also possible to use the most common probability distributions. Currently, the following ones are available.

Probability distributions
	All intervals of the same length on the distribution's support are equally probable in the uniform distribution.
	The normal distribution is determined by its mean μ and standard deviation σ. It is widely used in natural science, among other fields.
	The exponential distribution is the probability distribution that describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.
	The χ2 distribution with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables.
	Student's t-distribution arises when estimating the mean of a normally distributed population in situations where the sample size is small, and population standard deviation is unknown.
	The Bernoulli distribution is the probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q=1-p.
	The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes-no question, i.e. each ruled by the same Bernoulli distribution.
	The geometric distribution with parameter p is the discrete probability distribution of the number of failures before the first success. A Bernoulli variable rules each try with the parameter p.
	The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.
	The F-distribution is a continuous probability distribution that frequently arises as to the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.

Moreover, we can get a random number following such distributions, obtain its distribution and density function and find the quantile of given probability.

Probability functions
	It retrieves a random number following a given distribution.
	Distribution function of a random variable at a given point. In some cases, the analytical expression is given. distribution(X,x)=FX(x)=P(X≤x)=∫-∞xfX(t)dt, cumulative distribution function (CDF)
	Density function of a random variable at a given point. In some cases, the analytical expression is given. density(X,x)=fX(x)=ddxFX(x), probability density function (PDF).
	Quantile function of a random variable for a given probability. quantile(X,p)=x⟺distribution(X,x)=p, inverse function of CDF.

Probability distributions

Related Articles