INVERTED GOMPERTZ DISTRIBUTION: PROPERTIES AND ESTIMATION | ||||
| المجلة العلمية لقطاع کليات التجارة بجامعة الأزهر | ||||
| Article 10, Volume 9, Issue 1, 2012, Page 1-21 PDF (414.77 K) | ||||
| Document Type: المقالة الأصلية | ||||
| DOI: 10.21608/jsfc.2012.26368 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| Rabab E. Abd EL-Kader | ||||
| Rabab E. Abd EL-Kader, Amina E. Abu-Hussien and Soad A. AL-Gendy Department of Statistics, Faculty of Commerce, AL-Azhar University, Girls` Branch, Cairo, Egypt | ||||
| Abstract | ||||
| The inverted Gompertz distribution,and some of its properties are investigated. The distribution of the order statistic of the inverted Gompertz distribution and some special cases are presented. Transformed distributions of this distribution are derived. Based on Type II censored samples, the estimation of the shape and scale parameters, reliability and hazard rate functions are obtained using the maximum likelihood method. The uniformly minimum variance unbiased estimate of a function of the shape parameter is obtained assuming that the scale parameter is known. Asymptotic variances and covariances of the maximum likelihood estimators are found. Confidence intervals of the parameters are also given. Via a Monte Carlo simulation study, the estimated risks, squared bias and variances of the estimates are computed from different sample sizes. | ||||
Highlights | ||||
reliability function; hazard rate function; Type II censored samples; maximum likelihood method; uniformly minimum variance unbiased estimate. | ||||
| Keywords | ||||
| Inverted Gompertz distribution; Reliability function; hazard rate function; Type II censored samples; Maximum Likelihood Method; uniformly minimum variance unbiased estimate | ||||
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