Abstract
Moments of generalized order statistics appear in several areas of science and engineering. These moments are useful in studying properties of the random variables which are arranged in increasing order of importance, for example, time to failure of a computer system. The computation of these moments is sometimes very tedious and hence some algorithms are required. One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments. Generalized order statistics provides several models of ordered data as a special case. The moments of generalized order statistics also provide moments of order statistics and record values as a special case. In this research, the recurrence relations for single, product, inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution. These relations will be helpful for obtained moments of generalized order statistics from Lindley–Weibull distribution recursively. Special cases of the recurrence relations will also be obtained. Some characterizations of the distribution will also be obtained by using moments of generalized order statistics. These relations for moments and characterizations can be used in different areas of computer sciences where data is arranged in increasing order.
Highlights
Several situations arise where the ordering of the data is of great importance
The recurrence relations for single, product, inverse and ratio moments of generalized order statistics will be obtained for Lindley– Weibull distribution
We have derived expressions for recursive computation of single, product, inverse and ratio moments of gos when the sample is available from the Lindley–Weibull distribution
Summary
Several situations arise where the ordering of the data is of great importance. For example arrangement of Olympic records or magnitude of the earthquake measured on a Richter scale etc. The distributional properties of such data are studied by using specialized methods known as ordered random variables. Recurrence relations for moments of gos for a general class of probability distributions have been obtained by [7]. The relations for moments of gos for Marshall–Olkin extended Weibull distribution has been obtained by [8]. The recurrence relations for moments of gos for Kumaraswamy distribution have been obtained by [9]. The recurrence relations for moments of gos for Kumaraswamy Pareto distribution have been obtained by [11]. The relation (8) is very useful in recursive computation of moments of gos for the Lindley–Weibull distribution. Derive expressions for recursive computation of moments of gos when a sample from the Lindley–Weibull distribution is available
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