Properties of Doubly-Truncated Gamma Variables.
The truncated gamma distribution has been widely studied, primarily in life-testing and reliability settings. Most work has assumed an upper bound on the support of the random variable,i.e. the space of the distribution is (0,u). We consider a doubly-truncated gamma random variable restricted by both a lower (l) and upper (u) truncation point, both of which are considered known. We provide simple forms for the density, cumulative distribution function (CDF), moment generating function, cumulant generating function, characteristic function, and moments. We extend the results to describe the density, CDF, and moments of a doubly-truncated noncentral chi-square variable.
A-1124 Medical Center North, Dept of Preventive Medicine, Vanderbilt Univ. School of Med., Nashville, Tennessee 37232-2637.
Christopher S
CS
Coffey
3105C McGavran-Greenberg, Dept. of Biostatistics, CB#7400, University of North Carolina, Chapel Hill, North Carolina 27599.
Keith E
KE
Muller
censoring; characteristic function; internal pilot study; moments; noncentral chi-square