Why Is Really Worth Univariate Continuous Distributions

1007/978-1-4939-2818-7_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2817-0
Online ISBN: 978-1-4939-2818-7eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
Many probability distributions that are important in theory or applications have been visit site specific names. , statistical size distributions, actuarial distributions). org/10. This process is experimental and the keywords may be updated as the learning algorithm improves. Most are grouped and tabulated according to their support, and/or the distribution from which they are derived (e. g.

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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 variance are special cases of moments of distributions

the average, typical value of X

\mu = E(X) = \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.
This chapter enumerates those univariate continuous distributions find here represented as VGLMs/VGAMs and implemented in VGAM. This is a preview of subscription content, access via your institution.
For any set of independent random variables the probability density function of their joint distribution is the product of their individual density functions.

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, beta-type, gamma-type), and/or their purpose (e.
. These keywords were added by machine and not by the authors. 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. .