scholarly journals A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdullah M. Almarashi ◽  
Ali Algarni ◽  
Amal S. Hassan ◽  
M. Elgarhy ◽  
Farrukh Jamal ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Random Variables ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Independent Random Variables ◽  
Simple Random Sample ◽  
Simulation Research ◽  
Set Size ◽  
Median Ranked Set Sampling ◽  
Advanced Sampling

In this manuscript, we investigate the estimation of the unknown reliability measure R = P [Y < X], in the case where Y and X are two independent random variables with Topp–Leone distributions. As the main contribution, various advanced sampling strategies are studied. The suggested strategies are simple random, ranked set, and median ranked set samplings. Firstly, based on the maximum likelihood, we give an efficient estimator of R when the observations of the two random variables are selected from the same simple random sample. Secondly, such an estimator is addressed when the observations of the two random variables are selected from the ranked set sampling method. Then, based on median ranked set sampling, the maximum likelihood estimator of R is addressed in all the four cases. When the observations from the two random variables are selected from the same set size, two cases are considered, while the other two cases are considered at different set sizes. A simulation research is developed to evaluate the behavior of the obtained estimates based on standard and median ranked set samplings with their simple random sampling equivalents. The ratio of mean square error is used to assess the effectiveness of these estimates.

scholarly journals A Two-Parameter Model: Properties and Estimation under Ranked Sampling

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1214
Author(s):  
Rashad Bantan ◽  
Mahmoud Elsehetry ◽  
Amal S. Hassan ◽  
Mohammed Elgarhy ◽  
Dreamlee Sharma ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Simple Random Sampling ◽  
Quantile Function ◽  
Ranked Set Sampling ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Simple Random Sample ◽  
Alpha Power ◽  
Proposed Model ◽  
Comparison Results

This study introduces a flexible model with two parameters by combining the type II half-logistic-G family with the inverted Topp–Leone distribution. The proposed model is referred to as the half logistic inverted Topp–Leone (HLITL) distribution. The associated probability density function can be considered a mixture of the inverted Topp–Leone distributions. The proposed model can be deemed an acceptable model for fitting the right-skewed, reversed J-shaped, and unimodal data. The statistical properties, including the moments, Bonferroni and Lorenz curves, Rényi entropy, and quantile function, are derived. Additionally, the plots of the skewness and kurtosis measures are plotted based on the quantiles. The parameter estimators are implemented using the maximum likelihood method based on two sampling schemes: the simple random sample method and the ranked set sampling method. The proposed method is evaluated by using simulations. The results show that the maximum likelihood estimates of the parameters under ranked set sampling are more accurate than those under simple random sampling. Generally, there is good agreement between the theoretical and empirical results. Two real datasets are used to compare the HLITL model with the following models: alpha power exponential, alpha power Lindley, odd Fréchet inverse exponential, and odd Fréchet inverse Rayleigh models. The comparison results show that the HLITL model represents a better alternative lifetime distribution than the other competitive distributions.

scholarly journals Effectivity of Modified Maximum Likelihood Estimators Using Selected Ranked Set Sampling Data

2016 ◽  
Vol 38 (2) ◽  
Author(s):  
Tamanna Islam ◽  
Molla Rahman Shaibur ◽  
S.S. Hossain
Keyword(s):  
Maximum Likelihood ◽  
Ranked Set Sampling ◽  
Simple Random Sample ◽  
Exponential Distributions ◽  
Underlying Distribution ◽  
Population Mean ◽  
Scale Parameters ◽  
Modified Maximum Likelihood ◽  
Two Parameter ◽  
Better Than

This paper describes the modified maximum likelihood estimator (MMLE) of location and scale parameters based on selected ranked set sampling (SRSS) for normal, uniform and two-parameter exponential distributions. For these distributions, the MMLE of location and scale parameters for SRSS data were compared with the estimators of location and scale parameters for simple random sample (SRS) and ranked set sample (RSS). The MMLE based on SRSS data were found to be advantageous as compared to SRS and RSS estimators for the same number of measurements. The SRSS method with errors in ranking was also described. The minimum correlation between the actual and erroneous ranking was required for MMLE of SRSS to achieve better precision than usual SRS and RSS estimators. When the wrong assumption about the underlying distribution was present, the MMLE of the population mean based on SRSS was better than the RSS estimator ofthe population mean for all the cases considered.

Using ranked set sampling with extreme ranks in estimating the population proportion

2019 ◽  
Vol 29 (1) ◽  
pp. 165-177 ◽  
Author(s):  
Ehsan Zamanzade ◽  
M Mahdizadeh
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Finite Sample ◽  
Likelihood Estimator ◽  
Population Proportion ◽  
Health And Nutrition ◽  
Finite Sample Size ◽  
Using Data

This article studies the properties of the maximum likelihood estimator of the population proportion in ranked set sampling with extreme ranks. The maximum likelihood estimator is described and its asymptotic distribution is derived. Finite sample size properties of the estimator are investigated using simulation studies. It turns out that the proposed estimator is substantially more efficient than its simple random sampling and ranked set sampling analogs, as the true population proportion tends to zero/unity. The method is illustrated using data from the National Health and Nutrition Examination Survey.

scholarly journals Maximum likelihood estimation in location-scale families using varied L ranked set sampling

2020 ◽  
Author(s):  
Amer Al-Omari
Keyword(s):  
Maximum Likelihood ◽  
Random Sampling ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Sampling Schemes ◽  
Scale Parameters ◽  
Insight Into ◽  
Family Of Distributions

Recently, a generalized ranked set sampling (RSS) scheme has been introduced which encompasses several existing RSS schemes, namely varied L RSS (VLRSS), and it provides more precise estimators of the population mean than the estimators with the traditional simple random sampling (SRS) and RSS schemes. In this paper, we extend the work and consider the maximum likelihood estimators (MLEs) of the location and scale parameters when sampling from a location-scale family of distributions. In order to give more insight into the performance of VLRSS with respect to SRS and RSS schemes, the asymptotic relative precisions of the MLEs using VLRSS relative to that using SRS and RSS are compared for some usual location-scale distributions. It turns out that the MLEs with VLRSS are more precise than those with the existing sampling schemes.

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.

Maximum-likelihood estimators with known incidental parameters

1972 ◽  
Vol 72 (2) ◽  
pp. 233-241 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Random Variables ◽  
Maximum Likelihood Estimators ◽  
Independent Random Variables ◽  
Structural Parameter ◽  
Likelihood Methods ◽  
True Value ◽  
Incidental Parameters ◽  
Maximum Likelihood Methods

Suppose we have a sample of N independent random variables X1, …, XN where Xi has the distribution F(X|θ, øi). θ is a k-dimensional ‘structural’ parameter (θ(1), …, θ(k)), and the øi are scalar or vector ‘incidental’ parameters in some given space. The Xi may be scalar or vector random variables which are either discrete in which case we write f(X|θ, øi) for the probability associated with a given point, or else continuous random variables with a probability density f(X|θ, øi). In either case we sup pose the support of the probability distribution to be fixed. We aim to estimate the true value of θ by maximum-likelihood methods.

scholarly journals Even Order Ranked Set Sampling with Auxiliary Variable

2020 ◽  
Vol 18 (2) ◽  
Author(s):  
Muhammad Tayyab ◽  
Muhammad Noor ul-Amin ◽  
Muhammad Hanif
Keyword(s):  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Sampling Scheme ◽  
Ratio Estimator ◽  
Study Variable ◽  
Median Ranked Set Sampling ◽  
Even Order ◽  
Efficient Alternative ◽  
The One

Even order ranked set sampling (EORSS) is a novel proposed ranked set sampling scheme connected with an auxiliary variable correlated with the study variable. This scheme quantifies only the one sampling unit which is at even position from each ranking set by employing specific criteria. The performance of the ratio estimator under EORSS is compared to its contemporary estimators in simple random sampling (SRS), ranked set sampling (RSS), median ranked set sampling (MRSS) and quartile ranked set sampling (QRSS) exploiting the same number of quantified units. The simulation results proved that EORSS is an efficient alternative sampling scheme for ratio estimation than SRS, RSS, MRSS and QRSS.

scholarly journals Estimation of Stress-Strength Reliability For Weibull Distribution Based on Type-II Right Censored Ranked Set Sampling Data

2018 ◽  
pp. 781-806 ◽  
Author(s):  
Fatma Gül Akgül ◽  
Birdal ÅženoÄŸlu
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Efficient Estimation ◽  
Type Ii ◽  
Right Censored Data ◽  
Monte Carlo Simulation Study ◽  
Modified Maximum Likelihood

In this paper, we consider the estimation of stress-strength reliability  under the type-II right censored data when the distributions of both the stress and the strength are Weibull. First, we discuss the estimation of  based on simple random sampling (SRS). Then, we use the effective and the efficient alternative of SRS which is known to be the ranked set sampling (RSS) to estimate . In the estimation procedure of , we use two different approaches they are i) maximum likelihood (ML) which requires an iterative method and ii) modified maximum likelihood (MML) which has an explicit form. Monte-Carlo simulation study is performed to identify the efficient sampling method (i.e., SRS or RSS) and the efficient estimation method (i.e., ML or MML). Finally, strength and wind speed data sets are analyzed to illustrate the proposed methods in practice.

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