An Estimation of the Entropy for a Fréchet Distribution Based on Generalized Hybrid Censored Samples

In this paper, under generalized type-I hybrid censored samples; we derive the estimators for the entropy function of the Fréchet distribution. We also compare the introduced estimators in the sense of the relative mean squared error (RMSE) for various censored samples

Weibull-Linear Exponential Distribution and Its Applications

In this article, a new four-parameter lifetime distribution, namely, the Weibull-Linear exponential distribution is defined and studied. Several of its structural properties such as quartiles, moments, mean waiting time, mean residual lifetime, Renyi entropy, mode, and order statistics are derived. Based on the idea of the Weibull T − X family, the new density function of this model is developed. The model parameters, as well as some of the lifetime parameters (reliability and failure rate functions), are estimated using the maximum likelihood method. Asymptotic confidence intervals estimates of the model parameters are also evaluated by using the Fisher information matrix. Moreover, to construct the asymptotic confidence intervals of the reliability and failure rate functions, we need to find their variance of them, which are approximated by the delta method. A real data set is used to illustrate the application of the Weibull-Linear Exponential distribution

Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size

2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.We consider the problem of predictive interval for future observations from Weibull distribution. We consider two cases they are: (i) fixed sample size (FSS), (ii) random sample size (RSS). Further, we derive the predictive function for both FSS and RSS in closed forms. Next, the upper and lower 1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To show the usefulness of our results, we present some simulation examples. Finally, we apply our results to some real data set in life testing given in Lawless [16]

[[alternative]]The Interval Estimation of Parameters of Pareto Distribution and the Prediction Interval of the Future Observation for Progressively Type II Censored Sample

計畫編號：NSC94-2118-M032-004研究期間：200508~200607研究經費：346,000[[abstract]]有時因時間、成本的限制或資料蒐集時人為的疏失，而需面對不完整設限資料。若壽命分配之失敗率λ為具有尺度參數θ與形狀參數ν之Gamma分配，則此產品之壽命有柏拉圖分配, 其在壽命檢測與可靠度問題上佔據一個很重要的地位。所以本研究針對隨機移除之逐步型二設限樣本及隨機移除之一般化逐步型二設限樣本, 對具有尺度參數θ與形狀參數ν之雙參數型I柏拉圖分配之參數進行區間估計及信賴區域之研究. 同時提出未來觀測值和未來相鄰故障時間比值的預測區間。另外, 我們給一個數值例子來示範這些估計與預測結果,並用Monte Carlo模擬法,來評估這些估計與預測結果之表現. 查無英文摘要 distribution by progressively type Ⅱ censored sample or general progressively type Ⅱ censored sample with uniform removal or Binomial removal is investigated by individual confidence intervals or confidence regions. The distribution of the proposed pivotal quantities will be derived in this research. The future observation and the ratio of any two adjacent future lifetimes are predicted as well. One numerical example is given to demonstrate all results and the Monte Carlo simulation is used to assess the performance of all results based on the length of confidence interval or the area of confidence region under the confidence coefficient.[[sponsorship]]行政院國家科學委員