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Probability distributions
Reading time: 1minIt is also possible to use the most common probability distributions. Currently, the following ones are available.
| Probability distributions | |
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All intervals of the same length on the distribution's support are equally probable in the uniform distribution. |
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The normal distribution is determined by its mean μ and standard deviation σ. It is widely used in natural science, among other fields. |
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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. |
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The χ2 distribution with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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 | |
|---|---|
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It retrieves a random number following a given distribution. |
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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) |
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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). |
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Quantile function of a random variable for a given probability. quantile(X,p)=x⟺distribution(X,x)=p, inverse function of CDF. |