Distribution of the quotient of noncentral normal random variables
Titel:
Distribution of the quotient of noncentral normal random variables
Auteur:
Cabuk, Serafettin Springer, Melvin D.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 19 (1990) nr. 3 pagina's 1157-1168
Jaar:
1990
Inhoud:
The Mellin convolution is used to derive in analytical form an exact 3-parameterprobabilitydensity function of the quotient of two noncentral normal random variables. In contrast with the 5-parameter probability density function previously derivedby Fieller (1932) and Hinkley (1969), this 3-parameter probability density function is feasible for computer evaluation of the mean and cumulative distribution function, which are needed, for example, when dealing with estimation and distribution problems in regression analysis and sampling theory. When the normal variables are independent, the probability density function reduces to a 2-parameter function, for which a computer program is operational. An illustrative example is given for one set of parameters when the normal variables are independent, in which themean and functional form of the probability density function are presented, together with a brief tabulation of the probability density function.
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