Abstract
In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of function of generalized order statistics is discussed.
Highlights
A random variable X is said to have Erlang-truncated exponential distribution if its probability density function is of the form and the corresponding distribution function df is (2) where F x 1 F x .For more details on this distribution and its applications one may refer to [1]. k n 1 j 1 j n 1 i 1 F xi m f (3)i i 1; 0, Pfeifer’s record values 3].The marginal pdf of the r-th gos, X r, n, m, k,1 r n, is f X r,n,m,k x
The results for k-th record values and order statistics are deduced from the relations derived
Recurrence relations for marginal and joint moment generating functions of gos from power function distribution are derived by [7]. [8,9] have established recurrence relations for conditional and joint moment generating functions of gos based on mixed population, respectively. [10] has established explicit expressions and some recurrence relations for moment generating function of gos from Gompertz distribution
Summary
[4,5,6] have established recurrence relations for moment generating functions of record values from Pareto and Gumble, power function and extreme value distributions. Recurrence relations for marginal and joint moment generating functions of gos from power function distribution are derived by [7]. [8,9] have established recurrence relations for conditional and joint moment generating functions of gos based on mixed population, respectively. [10] has established explicit expressions and some recurrence relations for moment generating function of gos from Gompertz distribution. We establish exact expressions and some recurrence relations for marginal and joint moment generating functions of gos from Erlang-truncated exponential distribution. Results for order statistics and record values are deduced as special cases and a characterization of this distribution is obtained by using the conditional expectation of function of gos
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