Abstract
In this paper, we characterize doubly truncated classes of absolutely continuous distributions by considering the conditional expectation of functions of order statistics. Specific distributions considered as a particular case of the general class of distributions are Weibull, Pareto, Power function, Rayleigh and Inverse Weibull.
Highlights
In this paper, we characterize doubly truncated classes of absolutely continuous distributions by considering the conditional expectation of functions of order statistics
Let X1:n ≤ X2:n ≤ ...≤ Xn:n be the first n order statistics based on distribution with probability density function f(x) and cumulative fr s(x Xs:n=
The relation before doubly truncated case (Table 3). It was obtained recurrence relations based on order statistics without truncated and doubly truncated, and have been getting function of various distributions new by using certain parameters
Summary
We characterize doubly truncated classes of absolutely continuous distributions by considering the conditional expectation of functions of order statistics. Let X1:n ≤ X2:n ≤ ...≤ Xn:n be the first n order statistics based on distribution with probability density function (pdf) f(x) and cumulative fr s(x Xs:n= The doubly truncated pdf of X, say g(x), and cdf, say G(x), are given respectively by g= ( x) f (x) ,α ≤ ε < x < γ ≤ β , (1.3) Let X be an absolutely continuous random variables with pdf g(x), cdf G(x) and ∅(x) is a monotonic, continuous and differentiable function on (ε,γ).
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