Estimation of scale parameter of a Bivariate Lomax distribution by Ranked Set Sampling

2017 ◽  
Vol 12 (2) ◽  
pp. 107-113
Author(s):  
Rohan Dilip Koshti ◽  
Kirtee Kiran Kamalja
Keyword(s):  
Scale Parameter ◽  
Ranked Set Sampling ◽  
Lomax Distribution

Efficient Estimation of a Scale Parameter of Bivariate Lomax Distribution by Ranked Set Sampling

2021 ◽  
pp. 000806832199252
Author(s):  
Rohan D. Koshti ◽  
Kirtee K. Kamalja
Keyword(s):  
Scale Parameter ◽  
Real Life ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Efficient Estimation ◽  
Study Variable ◽  
Variable Formula ◽  
Lomax Distribution ◽  
Efficiency Comparison ◽  
Ams Classification

Ranked set sampling (RSS) is an efficient technique for estimating parameters and is applicable whenever ranking on a set of sampling units can be done easily by a judgment method or based on an auxiliary variable. In this paper, we assume [Formula: see text]to have bivariate Lomax distribution where a study variable [Formula: see text]is difficult and/or expensive to measure and is correlated with an auxiliary variable [Formula: see text] which is readily measurable. The auxiliary variable is used to rank the sampling units. In this article, we propose an estimator for the scale parameter of bivariate Lomax distribution using some of the modified RSS schemes. Efficiency comparison of the proposed estimators is performed numerically as well as graphically. A simulation study is also performed to demonstrate the performance of the proposed estimators. Finally, we implement the results to real-life datasets. AMS classification codes: 62D05, 62F07, 62G30

scholarly journals A flexible ranked set sampling schemes: Statistical analysis on scale parameter

2020 ◽  
Vol 9 (1) ◽  
pp. 189-203
Author(s):  
Abbas Eftekharian ◽  
Mostafa Razmkhah ◽  
Jafar Ahmadi
Keyword(s):  
Maximum Likelihood ◽  
Existence And Uniqueness ◽  
Sampling Methods ◽  
Scale Parameter ◽  
Likelihood Estimation ◽  
Ranked Set Sampling ◽  
Likelihood Estimator ◽  
Normal Distributions ◽  
Sampling Schemes ◽  
The Cost

A flexible ranked set sampling scheme including some various existing sampling methods  is proposed. This scheme may be used to minimize the  error of ranking and the cost of sampling. Based on the data obtained from this scheme, the maximum likelihood estimation as well as the Fisher information are studied for the  scale family of distributions. The existence and uniqueness of  the  maximum likelihood estimator  of the scale parameter of the exponential  and  normal distributions are  investigated. Moreover, the optimal scheme is derived via simulation and numerical computations.

scholarly journals Zubair Lomax Distribution: Properties and Estimation Based on Ranked Set Sampling

2020 ◽  
Vol 65 (3) ◽  
pp. 2169-2187
Author(s):  
Rashad Bantan ◽  
Amal S. Hassan ◽  
Mahmoud Elsehetry
Keyword(s):  
Ranked Set Sampling ◽  
Lomax Distribution

scholarly journals Reliability Estimation of Inverse Lomax Distribution Using Extreme Ranked Set Sampling

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Amer Ibrahim Al-Omari ◽  
Amal S. Hassan ◽  
Naif Alotaibi ◽  
Mansour Shrahili ◽  
Heba F. Nagy
Keyword(s):  
Ranked Set Sampling ◽  
Reliability Estimation ◽  
Simple Random Sample ◽  
Stress Distributions ◽  
Reliability Estimate ◽  
Lomax Distribution ◽  
Set Size ◽  
Reliability Estimates ◽  
Inverse Lomax Distribution ◽  
Extreme Ranked Set Sampling

In survival analysis, the two-parameter inverse Lomax distribution is an important lifetime distribution. In this study, the estimation of R = P   Y < X is investigated when the stress and strength random variables are independent inverse Lomax distribution. Using the maximum likelihood approach, we obtain the R estimator via simple random sample (SRS), ranked set sampling (RSS), and extreme ranked set sampling (ERSS) methods. Four different estimators are developed under the ERSS framework. Two estimators are obtained when both strength and stress populations have the same set size. The two other estimators are obtained when both strength and stress distributions have dissimilar set sizes. Through a simulation experiment, the suggested estimates are compared to the corresponding under SRS. Also, the reliability estimates via ERSS method are compared to those under RSS scheme. It is found that the reliability estimate based on RSS and ERSS schemes is more efficient than the equivalent using SRS based on the same number of measured units. The reliability estimates based on RSS scheme are more appropriate than the others in most situations. For small even set size, the reliability estimate via ERSS scheme is more efficient than those under RSS and SRS. However, in a few cases, reliability estimates via ERSS method are more accurate than using RSS and SRS schemes.

scholarly journals Estimation of Scale Parameter of Weibull-Lomax distribution via Bayesian Approach

2021 ◽  
Vol 09 (05) ◽  
Author(s):  
Arun Kumar Rao, ◽  
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Approach ◽  
Scale Parameter ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Lomax Distribution ◽  
Squared Error

In this paper, the Weibull-Lomax distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

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