Discrete Weibull distribution: different estimation methods under ranked set sampling and simple random sampling

2021 ◽  
pp. 1-23
Author(s):  
Cesar Augusto Taconeli ◽  
Idemauro Antonio Rodrigues de Lara
Keyword(s):  
Weibull Distribution ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Estimation Methods

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).

Stratified Ranked Set Sampling With Missing Observations for Estimating the Difference

2022 ◽  
pp. 209-232
Author(s):  
Carlos N. Bouza-Herrera
Keyword(s):  
Random Sampling ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Missing Observations ◽  
Seminal Paper ◽  
Sample Error ◽  
The Difference ◽  
Stratified Ranked Set Sampling ◽  
Stratified Model

The authors develop the estimation of the difference of means of a pair of variables X and Y when we deal with missing observations. A seminal paper in this line is due to Bouza and Prabhu-Ajgaonkar when the sample and the subsamples are selected using simple random sampling. In this this chapter, the authors consider the use of ranked set-sampling for estimating the difference when we deal with a stratified population. The sample error is deduced. Numerical comparisons with the classic stratified model are developed using simulated and real data.

Ratio-Type Estimation Using Scrabled Auxiliary Variables in Stratification Under Simple Random Sampling and Ranked Set Sampling

2022 ◽  
pp. 62-85
Author(s):  
Carlos N. Bouza-Herrera ◽  
Jose M. Sautto ◽  
Khalid Ul Islam Rather
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Auxiliary Variables ◽  
Mild Conditions ◽  
Squared Error ◽  
The Mean ◽  
Better Than

This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.

scholarly journals Estimating Bark Eating Caterpillars Indarbela quadrinotata (walker) in Populus deltoides Using Ranked Set Sampling

2020 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Arvind Kumar ◽  
Girish Chandra ◽  
Sanjay Kumar
Keyword(s):  
Random Sampling ◽  
Populus Deltoides ◽  
Insect Pest ◽  
Uttar Pradesh ◽  
Simple Random Sampling ◽  
Forest Tree ◽  
Ranked Set Sampling ◽  
Actual Measurement ◽  
Mean And Variance ◽  
Cost Efficient

<p>The problem of bark eating caterpillar, <em>Indarbela quadrinotata</em> infestation has been observed from variety of horticulture and forest tree species in India. The estimation of infestation of this caterpillar using conventional sampling methods was found difficult because counting the number of caterpillar in each tree is practically not feasible. Ranked set sampling (RSS) is a cost efficient method which provides improved estimators of mean and variance when actual measurement of the observations is difficult to obtain but a reasonable ranking of the units in the sample is relatively easy. In the present study, poplar, <em>Populus deltoides</em> plantation of Western Uttar Pradesh and Uttarakhand was taken for the assessment of <em>Indarbela quadrinotata</em> infestation. The RSS estimator of population mean and variance have been discussed and compared with the corresponding estimators from simple random sampling (SRS). The relative precision (RP) of RSS procedure with respect to the SRS for four different set sizes of <em>k </em>= 3, 5, 7, and 10 has been deliberated. It was seen that RP increase with the increment in <em>k</em>. The method of RSS was found suitable for the assessment of insect pest infestation.</p><p><strong>Keywords</strong><strong>: </strong><em>Indarbela quadrinotata</em>, <em>Populus deltoides</em>, simple random sampling, ranked set sample, order statistics.</p>

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.

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