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In probability theory and statistics, an inverse distribution is the distribution of the reciprocal of a random variable. Inverse distributions arise in particular in the Bayesian context of prior distributions and posterior distributions for scale parameters .
The inverse Gaussian distribution is a two-parameter exponential family with natural parameters −λ/(2μ 2) and −λ/2, and natural statistics X and 1/X.. For > fixed, it is also a single-parameter natural exponential family distribution [3] where the base distribution has density
The normal distribution is perhaps the most important case. Because the normal distribution is a location-scale family, its quantile function for arbitrary parameters can be derived from a simple transformation of the quantile function of the standard normal distribution, known as the probit function. Unfortunately, this function has no closed ...
In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality (+) = + is always true in elementary algebra.
By definition, a distribution on is a continuous linear functional on (). Said differently, a distribution on U {\displaystyle U} is an element of the continuous dual space of C c ∞ ( U ) {\displaystyle C_{c}^{\infty }(U)} when C c ∞ ( U ) {\displaystyle C_{c}^{\infty }(U)} is endowed with its canonical LF topology.
The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central and where types of departure from this include: mounded (or unimodal), U-shaped, J-shaped, reverse-J shaped and multi-modal. [1] A bimodal distribution would have two high points rather than one. The shape of a distribution is ...
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution. It has the cumulative distribution function It has the cumulative distribution function
In this formalization, the bivariate distribution of X 1 and X 2 is said to exhibit regression toward the mean if, for every number c > μ, we have μ ≤ E[X 2 | X 1 = c] < c, with the reverse inequalities holding for c < μ. [20] [21] The following is an informal description of the above definition. Consider a population of widgets.