scholarly journals Inference on Exponentiated Power Lindley Distribution Based on Order Statistics with Application

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mansour Shrahili ◽  
Naif Alotaibi ◽  
Devendra Kumar ◽  
A. R. Shafay
Keyword(s):  
Order Statistics ◽  
Real Data ◽  
Linear Functions ◽  
Lindley Distribution ◽  
Scale Parameters ◽  
Power Lindley Distribution ◽  
Censored Sample ◽  
Best Linear Unbiased ◽  
Edgeworth Approximation ◽  
Mean Variance

Exponentiated power Lindley distribution is proposed as a generalization of some widely well-known distributions such as Lindley, power Lindley, and generalized Lindley distributions. In this paper, the exact explicit expressions for moments of order statistics from the exponentiated power Lindley distribution are derived. By using these relations, the best linear unbiased estimates of the location and scale parameters, based on type-II right-censored sample, are obtained. Next, the mean, variance, and coefficients of skewness and kurtosis of some certain linear functions of order statistics are calculated and then used to derive the approximate confidence interval for the location and scale parameters using the Edgeworth approximation. Finally, some numerical illustrations and two real data applications are presented.

scholarly journals Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2080
Author(s):  
E. H. Hafez ◽  
Fathy H. Riad ◽  
Sh. A. M. Mubarak ◽  
M. S. Mohamed
Keyword(s):  
Real Data ◽  
Upper And Lower Bounds ◽  
Type Ii ◽  
Research Project ◽  
Data Set ◽  
Lindley Distribution ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests ◽  
Censored Sample

Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, ψ and ζ. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.

scholarly journals Weighted Moments Estimators of the Parameters for the Extreme Value Distribution Based on the Multiply Type II Censored Sample

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Jong-Wuu Wu ◽  
Sheau-Chiann Chen ◽  
Wen-Chuan Lee ◽  
Heng-Yi Lai
Keyword(s):  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Estimation Methods ◽  
Type Ii ◽  
Scale Parameters ◽  
Censored Sample ◽  
Best Linear Unbiased ◽  
Moments Estimators ◽  
Type Ii Censored Sample

We propose the weighted moments estimators (WMEs) of the location and scale parameters for the extreme value distribution based on the multiply type II censored sample. Simulated mean squared errors (MSEs) of best linear unbiased estimator (BLUE) and exact MSEs of WMEs are compared to study the behavior of different estimation methods. The results show the best estimator among the WMEs and BLUE under different combinations of censoring schemes.

Estimation of the Parameters of Triangular Distribution by Order Statistics

2003 ◽  
Vol 54 (1-2) ◽  
pp. 45-56 ◽  
Author(s):  
Philip Samuel ◽  
P. Yageen Thomas
Keyword(s):  
Order Statistics ◽  
Triangular Distribution ◽  
Unbiased Estimators ◽  
Product Moments ◽  
Scale Parameters ◽  
U Statistics ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators ◽  
Moments Of Order Statistics ◽  
Single And Product Moments

In this paper, we derive explicit expressions for the single and product moments of order statistics arising from the standard triangular distribution. Best linear unbiased estimators of the location and scale parameters of a triangular distribution based on order statistics are obtained. The efficiencies of these estimators are also compared with estimators based on U-statistics

Bayesian and non-Bayesian inference under adaptive type-II progressive censored sample with exponentiated power Lindley distribution

2021 ◽  
pp. 1-21
Author(s):  
Hanan Haj Ahmad ◽  
Mukhtar M. Salah ◽  
M. S. Eliwa ◽  
Ziyad Ali Alhussain ◽  
Ehab M. Almetwally ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Type Ii ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Censored Sample

scholarly journals The Weighted Power Lindley Distribution with Applications on the Life Time Data

2020 ◽  
pp. 225-237
Author(s):  
Aafaq A. Rather ◽  
Gamze Özel
Keyword(s):  
Information Matrix ◽  
Life Time ◽  
Real Data ◽  
Data Sets ◽  
Lifetime Data ◽  
Time Data ◽  
Data Set ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
New Distribution

In this paper, we have proposed a new version of power lindley distribution known as weighted power lindley distribution. The different structural properties of the newly model have been studied. The maximum likelihood estimators of the parameters and the Fishers information matrix have been discussed. It also provides more flexibility to analyze complex real data sets.  An application of the model to a real data set is analyzed using the new distribution, which shows that the weighted power Lindley distribution can be used quite effectively in analyzing real lifetime data.

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