From Latin to Modern French by Mildred K. Pope

By Mildred K. Pope

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K, G Iy (s) = L P·qk+·S~/L Piqk+i' x -x i ~ ~ i 36 ADRIENNE W. KEMP AND C. D. KEMP where X - Y = k; we note that conditional distributions for Y given Y-X ~o not need se~arate consideration since Gy1y_x(s) L p. s /L p. kqi i ~- i ~ ~- = s G Iy (s). x -x When X and Y have binomial distributions with parameters (n,p) and (m,p) respectively, then the conditional distribution for X given X + Y is of course hyper geometric (Type IA). And when X and Yare both negative-binomial with parameters (u,q) and (v,q) the conditional distribution for X given X + Y is negative hypergeometric (Type II/IlIA).

From the results of Joshi (1972), extended by Charalambides (1973b), ea is estimable for any integer a > 0, and we have the following [cf. 5)]. 3. On the basis of k independent random samples Xl.. •. , i=l, •.. ,k where X .. 1) with N l. J = 00, there exists a unique mvue of e a which is a function of (X,Y). , - " " Proof. 9). m < (v,y) < x. 11) 26 T. -I "- S (x,y) a II S(x-j,y). 13) This points out a difference between the mvue Sa. of Sa. 13), a. ) = [S~(x'r)] a. The mvue of ea. when the truncation vector p is assumed known is easily found to be [cf.

S are 2Fl[1,1-n; l-n; s]/2Fl[1,1-n; l-n; 1] = 2Fl[1,1-n; 2; l-s] and 1 1 1 1 1 2 Fl[-n, 2; -n+z; s]/2 Fl I-n,z; -n+z; 1] = 2FlI-n,Z; 1; l-s] respectively, where n is a positive integer (as throughout the paper). 2Fl[m-n+l,l; m+n; 1], m + 1 > n > 1. 3. URN MODELS AND CONTAGION MODELS. For integer values of the parameters Types IA and IIA are particular Polya distributions (Type IA is hypergeometric and Type IIA negative hypergeometric) , whilst Types IlIA and IV are instances of the inverse Polya distribution (Type IIA is inverse hypergeometric and Type IV inverse hypergeometric with additional replacements).

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