My libraryIn statistics, a univariate distribution is a probability distribution of only one random variable.
C is called a normalising constant
density core of f(x) can be called g
The pdf and cdf are related;
F(x) = \integral f(x)
The mean and More Info are special cases of moments of distributions
the average, typical value of X
\mu = E(X) click for more info \int_x_b
The mean is also known as the the first moment of a distribution
the second and third moments;
E(X^2) E(X^3)
central moments about the mean
@todo
Variance is the second central moment of a distribution
\mu_2
V(X) is the
a single formula for the moments of all r
the moment generating function mgf
@todo – Linearity of expectation is true only for finite sums?
Quantile function is the inverse of the cumulative distribution function
is written as X^2(v)
parameter is the degrees of freedom
The exponential distribution M(\lambda) is a special case of the X^2(v)
Student’s t distribution, t(v)
a special case of the t-distribution is the cauchy distribution with v=1
none of the moments of the Cauchy distribution exist, hence some of the general results such as the Central limit theorem do no apply.
Search the world’s most comprehensive index of full-text books. The distributions of continuous random variables are described by the probability distribution functions (pdfs) and cumulative distribution functions (cdfs)
should integrate to 1
non-negative
any mathematical function which is non-negative, positive on at least one interval of values of x, and has a finite integral can be made into a pdf.
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This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables).
Other examples of discrete univariate distributions include the binomial, geometric, negative binomial, and Poisson distributions.
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Examples of commonly applied continuous univariate distributions3 include the normal distribution, Student’s t distribution, chisquare distribution, F distribution, exponential and gamma distributions. 1 At least 750 univariate discrete distributions have a peek at these guys been reported in the literature.
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The univariate continuous uniform distribution on an interval [a, b] has the property that all sub-intervals of the same length are equally likely.
One of the simplest examples of a discrete univariate distribution is the discrete uniform distribution, where all elements of a finite set are equally likely. It is the probability model for the outcomes of tossing a fair coin, rolling a fair die, etc. .