Upper Record Values from Extended Exponential Distribution

Abstract

Some recurrence relations are established for the single and product moments of upper record values for the extended exponential distribution by Nadarajah and Haghighi (2011) as an alternative to the gamma, Weibull, and the exponentiated exponential distributions. Recurrence relations for negative moments and quotient moments of upper record values are also obtained. Using relations of single moments and product moments, means, variances, and covariances of upper record values from samples of sizes up to 10 are tabulated for various values of the shape parameter and scale parameter. A characterization of this distribution based on conditional moments of record values is presented.

Best Linear Unbiased Estimation and Prediction of Record Values Based on Kumaraswamy Distributed Data

“…Other forms have been introduced by Arnold et al [3], which will make calculating the formulas from ( 11) to (15) easier. The values of c i and d i that we introduced in formulas ( 11) and ( 12) to find their values, will be the outcomes of the following matrix…”

“…While, the values of the formulas from ( 13) to (15) are simply the outcomes of the following matrix…”

“…Many of them introduced some methods to do so like Arnold et al [3], Ahsanullah [2] and Balakrishnan and Cohen [4] by estimating the parameters then predicting a future record value. Some other authors apply these methods to different distributions such as Kumar [15], Singh et al [22], Chacko and Shy Mary ( [6], [7]) and Barakat et al [5].…”