Estimation of the location and scale parameters of generalized exponential distribution based on order statistics. (English) Zbl 1151.62309
Summary: In this paper we consider the generalized exponential distribution with known shape parameter \(\Theta\). We first derive the exact forms of means, variances and covariances of order statistics. We use these expressions in obtaining the necessary coefficients for the best linear unbiased estimators of the location and scale parameters for \(\Theta =0.5\,(0.5)\,5.0\) and for sample sizes up to ten. The variances and covariances of these estimators are also given.
Keywords:
Generalized exponential distribution; Order statistics; Moments of order statistics; Digamma, polygamma and hypergeometric functions; Location and scale parameters; Best linear unbiased estimatorsReferences:
| [1] | Arnold B.C., A First Course in Order Statistics (1992) · Zbl 0850.62008 |
| [2] | David H. A., Order Statistics (1981) · Zbl 0553.62046 |
| [3] | DOI: 10.1111/1467-842X.00072 · Zbl 1007.62503 · doi:10.1111/1467-842X.00072 |
| [4] | Joshi P.C., Sankhyā 39 pp 362– (1978) |
| [5] | DOI: 10.1016/0378-3758(82)90051-9 · Zbl 0473.62042 · doi:10.1016/0378-3758(82)90051-9 |
| [6] | Mathai A.M., A Handbook of Generalized Special Functions for Statistical and Physical Sciences (1993) · Zbl 0770.33001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
