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 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 Estimation of the Exponential Pareto Distribution’s Parameters under Ranked and Double Ranked Set Sampling Designs

2021 ◽  
pp. 169-184
Author(s):  
Mohamed H. Sabry ◽  
Ehab Mohamed Almetwally
Keyword(s):  
Random Sampling ◽  
Relative Efficiency ◽  
Pareto Distribution ◽  
Likelihood Function ◽  
Maximum Likelihood Estimators ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Mean Square ◽  
Distribution Parameters ◽  
Mean Square Errors

In this paper, the derivation of the likelihood function for parameter estimation based on double ranked set sampling (DRSS) designs used by Sabry el.al.; (2019) for the estimation of the parameters of the power generalized Weibull distribution is considered. The developed likelihood function is then used for the estimation of the exponential Pareto distribution parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) designs. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different designs. The relative efficiency of the DRSS estimates with respect to other designs was found to be higher in case of the exponential Pareto distribution (EP).

scholarly journals Parameter Estimation Based on Double Ranked Set Samples with Applications to Weibull Distribution

2022 ◽  
Vol 19 (1) ◽  
pp. 2-24
Author(s):  
Mohamed Abd Elhamed Sabry ◽  
Hiba Zeyada Muhammed ◽  
Mostafa Shaaban ◽  
Abd El Hady Nabih
Keyword(s):  
Parameter Estimation ◽  
Weibull Distribution ◽  
Random Sampling ◽  
Likelihood Function ◽  
Maximum Likelihood Estimators ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Distribution Parameters ◽  
Two Parameters ◽  
Mean Square Errors

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating the two parameters of the Weibull distribution (WD).

scholarly journals ANALISIS EFISIENSI TEKNIS USAHATANI PADI SAWAH

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Dean Riza Rivanda ◽  
Wini Nahraeni ◽  
Arti Yusdiarti
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Random Sampling ◽  
Likelihood Estimation ◽  
Simple Random Sampling

ABSTRAKPenelitian ini bertujuan untuk mengetahui dan menganalisis faktor-faktor yang mempengaruhi produksi dan tingkat efisiensi teknis padi sawah. Pengumpulan data dilaksanakan pada bulan Desember 2013 – Januari 2014 di Kecamatan Telagasari Kabupaten Karawang. Petani sampel berjumlah 50 orang dan dipilih dengan menggunakan metode simple random sampling. Metode analisis data yang digunakan adalah Fungsi Produksi Stohactic Frontier Cobb-Douglas yang diolah dengan menggunakan aplikasi Frontier 4.1c menggunakan metode Maximum Likelihood Estimation (MLE). Hasil penelitian menunjukkan bahwa variabel luas lahan, pupuk NPK, pupuk kandang, tenaga kerja, musim tanam, serta pestisida masing-masing berpengaruh positif terhadap produksi padi sawah sedangkan jumlah benih berpengaruh negatif. Secara statistik semua variabel berpengaruh nyata pada selang kepercayaan diatas 10 persen, kecuali pestisida. Tingkat efisiensi teknis petani di daerah penelitian telah efisien secara teknis, dengan efisiensi teknis (ET) rata-rata mencapai 75 persen dengan tingkat ET tertinggi 95 persen dan terendah 43 persen. Faktor penyuluhan dan pendidikan mampu menurunkan efek inefisiensi teknis atau dapat meningkatkan efisiensi usahatani padi. Walaupun variabel status kepemilikan lahan dan pengalaman meningkatkan inefisiensi, namun secara statistik tidak signifikan dan hanya variabel status kepemilikan lahan yang signifikan terhadap inefisiensi teknis.

On Estimating Population Means of Two-Sensitive Variables With Ranked Set Sampling Design

2022 ◽  
pp. 42-61
Author(s):  
Agustin Santiago Moreno ◽  
Khalid Ul Islam Rather
Keyword(s):  
Empirical Evidence ◽  
Simulation Study ◽  
Random Sampling ◽  
Relative Efficiency ◽  
Convex Combination ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Population Means ◽  
Sampling Schemes

In this chapter, the authors consider the problem of estimating the population means of two sensitive variables by making use ranked set sampling. The final estimators are unbiased and the variance expressions that they derive show that ranked set sampling is more efficient than simple random sampling. A convex combination of the variance expressions of the resultant estimators is minimized in order to suggest optimal sample sizes for both sampling schemes. The relative efficiency of the proposed estimators is then compared to the corresponding estimators for simple random sampling based on simulation study and real data applications. SAS codes utilized in the simulation to collect the empirical evidence and application are included.

scholarly journals Generalized Exponential Distribution - Estimation of parameters using modifications in methods of Ranked Set Sampling

2021 ◽  
Author(s):  
Vyomesh Prahlad Nandurbarkar ◽  
Ashok Shanubhogue
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Exponential Distribution ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Likelihood Method ◽  
Generalized Exponential Distribution ◽  
Data Set ◽  
Extreme Ranked Set Sampling

Abstract In this study, we estimate the parameters of the Generalized Exponential Distribution using Moving Extreme Ranked Set Sampling (MERSS). Using the maximum likelihood estimation method, we derive the expressions. MERSS estimates are compared with estimates obtained by simple random sampling (SRS) using a real data set. We also study the other variations of the methods of Ranked Set Sampling like Quartile Ranked Set Sampling(QRSS), Median Ranked Set Sampling(MRSS) and Flexible Ranked Set Sampling(FLERSS) (a scheme based on QRSS and MRSS). For known shape parameter values, we present coefficients for linear combinations of order statistics for least squares estimates. Here, the expressions are derived through maximum likelihood, and the estimates are calculated numerically. Simulated results indicate that estimates generated using least-squares and the maximum likelihood method for Ranked Set Sampling (RSS) perform better than those generated using Simple Random Sampling (SRS). Asymptotically, MERSS outperforms SRS, QRSS, MRSS, and FLERSS.

scholarly journals The Generalized Odd Gamma-G Family of Distributions: Properties and Applications

2018 ◽  
Vol 47 (2) ◽  
pp. 69-89 ◽  
Author(s):  
Bistoon Hosseini ◽  
Mahmoud Afshari ◽  
Morad Alizadeh
Keyword(s):  
Maximum Likelihood ◽  
Test Validity ◽  
Estimation Method ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Data Sets ◽  
Maximum Likelihood Estimation Method ◽  
Family Of Distributions

Recently, new continuous distributions have been proposed to apply in statistical analysis. In this paper, the Generalized Odd Gamma-G distribution is introduced. In particular, G has been considered as the Uniform distribution and some statistical properties such as quantile function, asymptotics, moments, entropy and order statistics have been calculated.The fitness capability of this model has been investigated  by fitting this model and others based on real data sets. The  parameters of this model are estimated by the maximum likelihood estimation method with simulated  real data in order to test validity of maximum likelihood estimators .

On Estimating Population Means of Two-Sensitive Variables With Ranked Set Sampling Design

2022 ◽  
pp. 104-140
Author(s):  
Shivacharan Rao Chitneni ◽  
Stephen A. Sedory ◽  
Sarjinder Singh
Keyword(s):  
Empirical Evidence ◽  
Simulation Study ◽  
Random Sampling ◽  
Relative Efficiency ◽  
Convex Combination ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Population Means ◽  
Sampling Schemes

In the chapter, the authors consider the problem of estimating the population means of two sensitive variables by making use of ranked set sampling. The final estimators are unbiased and the variance expressions that they derive show that ranked set sampling is more efficient than simple random sampling. A convex combination of the variance expressions of the resultant estimators is minimized in order to suggest optimal sample sizes for both sampling schemes. The relative efficiency of the proposed estimators is then compared to the corresponding estimators for simple random sampling based on simulation study and real data applications. SAS codes utilized in the simulation to collect the empirical evidence and application are included.

ON EXTROPY PROPERTIES AND DISCRIMINATION INFORMATION OF DIFFERENT STRATIFIED SAMPLING SCHEMES

2021 ◽  
pp. 1-16
Author(s):  
Abbas Eftekharian ◽  
Guoxin Qiu
Keyword(s):  
Random Sampling ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Stochastic Orders ◽  
Data Sets ◽  
Sampling Schemes ◽  
Discrimination Information ◽  
Imperfect Ranking ◽  
Stratified Ranked Set Sampling ◽  
Better Than

Ranked set sampling (RSS) and some of its variants are sampling designs that are applied widely in different areas. When the underlying population contains different subpopulations, we can use stratified ranked set sampling (SRSS) which combines the advantages of stratification with RSS. In the present paper, we consider the information content of SRSS in terms of extropy measure. Some results using stochastic orders properties are obtained. The effect of imperfect ranking on discrimination information is analytically investigated. It is proved that discrimination information between the perfect SRSS and simple random sampling (SRS) data sets performs better than that of between the imperfect SRSS and SRS data sets.

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