ghyper.types

Generalized hypergeometric types as given by Kemp and Kemp

distribution

Ten distributions supplementing those built into R. Inverse Gauss, 
	Kruskal-Wallis, Kendall's Tau, Friedman's chi squared, Spearman's rho, maximum F ratio, 
	the Pearson product moment correlation coefficiant, Johnson distributions, nommal scores 
	and generalized hypergeometric distributions. In addition two random number generators
	of George Marsaglia are included.

Bob Wheeler

SuppDists

Supplementary distributions

ghyper.types function

The basic representation is in terms of a two-way table:<tabular>ccc</tabular>{
x 	k-x 	k a-x 	b-k+x 	N-k a 	b 	N
}and the associated hypergeometric probability $P(x)=C_x^a C_{k-x}^b / C_k^N$.The types are classified according to ranges of a, k, and N.

Two-way table

Minor modifications in the definition of three of the types have been made to avoid numerical difficulties. Note, J denotes a nonnegative integer.
<tabular>ll</tabular>{
[Classic] 		$0<a, 0<n,="" 0<k$="" integers:="" a,="" n,="" k.="" $max(0,a+k-n)="" \le="" x="" min(a,k)$="" [ia(i)]="" (real="" classic)="" at="" least="" one="" noninteger="" parameter="" $0<a,="" 0<k,="" k-1<a<n-(k-1)$="" integer:="" k="" $0="" a$="" [ia(ii)]="" a-1<k<n-(a-1)$="" a="" interchanging="" and="" transforms="" this="" to="" type="" ia(i)="" [ib]="" a+k-1<n,="" j="" <="" (a,k)="" j+1$="" j$="" non-integer:="" \dots$="" note:="" kemp="" specify="" $-1<n$.="" no="" practical="" applications="" for="" distribution.="" [iia]="" (negative="" hypergeometric)="" $a<0,="" n<a-1,0<k$="" k$="" $n<a,="" n="" \ne="" a-1$="" [iib]="" -1<n<k+a-1,="" (k,k+a-1-n)="" ....$="" is="" very="" strange="" special="" calculations="" were="" used.="" applications.="" [iiia]="" $0<a,n<k-1,k<0$="" iia="" $n<k,="" k-1$="" [iiib]="" $0<a,-1<n<a+k-1,k<0,="" j<(a,a+k-1-n)<j+1$="" non="" iib="" [iv]="" (generalized="" waring)="" $a<0,-1<n,="" k<0$="" \dots$<="" p="">}</a,>

ghyper.types: Kemp and Kemp generalized hypergeometric types

Description

Arguments

Two-way table

Kemp and Kemp types

References