= = = = +

Calculation of these estimates differs very little from the calculation of MMLE for IG samples. We select a first approximation p1 or (cxj = 2/~). which is then substituted into the first two equations of (7.2.10). These equations are then solved simultaneously for approximations -y(p 1) and f3(p 1). We enter a table of the gamma distribution cdf with the approximation cx~1 ) = 21~ and F = r!(N + I) and interpolate to read an approximation z~ 1J,. A corresponding estimate of the rth ordered variate Xr:N is then calculated as

(7.2.11) If E(X, N) = X,,N, then no further calculations are needed. Otherwise we continue with additional iterations until we are able to interpolate as shown below:

The likelihood function of a singly right truncated sample from a three-parameter gamma distribution with pdf (7 .2.1) is

"

a-y f3 ~~ 1 F(T) a-y a In L np I ~ . n aF(T) a[3 = - r3 + f32 ~~~ (X; - -y) - F(T) ~ = 0, (7.2. 13)