scholarly journals Comparative Study of New and Traditional Estimators of a New Lifetime Model

2021 ◽  
Vol 19 (1) ◽  
pp. 2-32
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay Kumar Singh ◽  
Umesh Singh
Keyword(s):  
Distribution Function ◽  
Least Squares ◽  
Coverage Probability ◽  
Weighted Least Squares ◽  
Mean Square ◽  
Lifetime Model ◽  
Anderson Darling ◽  
Von Mises ◽  
Methods Of Moments ◽  
Mean Square Errors

In this article, we have studied the behavior of estimators of parameter of a new lifetime model, suggested by Maurya et al. (2016), obtained by using methods of moments, maximum likelihood, maximum product spacing, least squares, weighted least squares, percentile, Cramer-von-Mises, Anderson-Darling and Right-tailed Anderson-Darling. Comparison of the estimators has been done on the basis of their mean square errors, biases, absolute and maximum absolute differences between empirical and estimated distribution function and a newly proposed criterion. We have also obtained the asymptomatic confidence interval and associated coverage probability for the parameter.

scholarly journals On the Burr XII-moment exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0246935
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Mustafa Ç. Korkmaz ◽  
Wenhui Sheng ◽  
Azeem Ali
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Simulation Studies ◽  
Conditional Moments ◽  
Mathematical Properties ◽  
Lifetime Model ◽  
Anderson Darling ◽  
Von Mises

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue life applications.

scholarly journals Reliability Properties of the NDL Family of Discrete Distributions with Its Inference

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1139
Author(s):  
Mohammed Mohammed Ahmed Almazah ◽  
Badr Alnssyan ◽  
Abdul Hadi N. Ahmed ◽  
Ahmed Z. Afify
Keyword(s):  
Least Squares ◽  
Negative Binomial ◽  
Weighted Least Squares ◽  
Sufficient Conditions ◽  
Real Life ◽  
Discrete Distributions ◽  
Real World Data ◽  
Life Problems ◽  
Anderson Darling ◽  
Von Mises

The natural discrete Lindley (NDL) distribution is an intuitive idea that uses discrete analogs to well-known continuous distributions rather than using any of the published discretization techniques. The NDL is a flexible extension of both the geometric and the negative binomial distributions. In the present article, we further investigate new results of value in the areas of both theoretical and applied reliability. To be specific, several closure properties of the NDL are proved. Among the results, sufficient conditions that maintain the preservation properties under useful partial orderings, convolution, and random sum of random variables are introduced. Eight different methods of estimation, including the maximum likelihood, least squares, weighted least squares, Cramér–von Mises, the maximum product of spacing, Anderson–Darling, right-tail Anderson–Darling, and percentiles, have been used to estimate the parameter of interest. The performance of these estimators has been evaluated through extensive simulation. We have also demonstrated two applications of NDL in modeling real-life problems, including count data. It is worth noting that almost all the methods have resulted in very satisfactory estimates on both simulated and real-world data.

scholarly journals A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 135 ◽  
Author(s):  
Ahmed Z. Afify ◽  
Osama Abdo Mohamed
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Mathematical Properties ◽  
Anderson Darling ◽  
Von Mises

In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates, and right-skewed, left-skewed, symmetrical, and reversed-J shaped densities. Some mathematical properties of the proposed distribution are derived. The model parameters are estimated via eight frequentist estimation methods called, the maximum likelihood estimators, least squares and weighted least-squares estimators, maximum product of spacing estimators, Cramér-von Mises estimators, percentiles estimators, and Anderson-Darling and right-tail Anderson-Darling estimators. Extensive simulations are conducted to compare the performance of these estimation methods for small and large samples. Four practical data sets from the fields of medicine, engineering, and reliability are analyzed, proving the usefulness and flexibility of the proposed distribution.

scholarly journals The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1684 ◽  
Author(s):  
Maha A. D. Aldahlan ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Finite Sample ◽  
Anderson Darling ◽  
Von Mises ◽  
Cramer Von Mises

In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution.

scholarly journals Statistical Inferences on Odd Fréchet Power Function Distribution

2021 ◽  
Author(s):  
Muhammad Ahsan ul Haq ◽  
Mohammed Albassam ◽  
Muhammad Aslam ◽  
Sharqa Hashmi
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Statistical Inferences ◽  
Proposed Model ◽  
Power Function Distribution ◽  
Anderson Darling ◽  
Von Mises

This article introduces a new unit distribution namely odd Fréchet power (OFrPF) distribution. Numerous properties of the proposed model including reliability analysis, moments, and Rényi Entropy for the proposed distribution. The parameters of the OFrPF distribution are obtained using different approaches such as maximum likelihood, least squares, weighted least squares, percentile, Cramer-von Mises, Anderson-Darling. Furthermore, a simulation was performed to study the performance of the suggested model. We also perform a simulation study to analyze the performances of estimation methods derived. The applications are used to show the practicality of OFrPF distribution using two real data sets. OFrPF distribution performed better than other competitive models.

scholarly journals The Poisson Nadarajah-Haghighi Distribution: Different Methods of Estimation

2021 ◽  
Author(s):  
Sajid Ali ◽  
Sanku Dey ◽  
M H Tahir ◽  
Muhammad Mansoor
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Distribution Functions ◽  
Absolute Difference ◽  
Unknown Parameters ◽  
Data Set ◽  
Bayes Estimates ◽  
Least Squares Estimators ◽  
Anderson Darling ◽  
Mean Square Errors

Estimation of parameters of Poisson Nadarajah-Haghighi (PNH) distribution from the frequentist and Bayesian point of view is discussed in this article. To this end, we briefly described ten different frequentist approaches, namely, the maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, minimum spacing absolute distance estimators, minimum spacing absolute-log distance estimators, Cramér-von Mises estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. To assess the performance of different estimators, Monte Carlo simulations are done for small and large samples. The performance of the estimators is compared in terms of their bias, root mean squares error, average absolute difference between the true and estimated distribution functions, and the maximum absolute difference between the true and estimated distribution functions of the estimates using simulated data. For the Bayesian inference of the unknown parameters, we use Metropolis–Hastings (MH) algorithm to calculate the Bayes estimates and the corresponding credible intervals. Results from the simulation study suggests that among the considered classical methods of estimation, weighted least squares and the maximum product spacing estimators uniformly produces the least biases of the estimates with least root mean square errors. However, Bayes estimates perform better than all other estimates. Finally, we discuss a practical data set to show the application of the distribution.

scholarly journals The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2060
Author(s):  
Mashail M. AL Sobhi
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Inverse Power ◽  
Model Parameters ◽  
Proposed Model ◽  
Anderson Darling ◽  
Von Mises ◽  
Insurance Data

The present paper proposes a new distribution called the inverse power logistic exponential distribution that extends the inverse Weibull, inverse logistic exponential, inverse Rayleigh, and inverse exponential distributions. The proposed model accommodates symmetrical, right-skewed, left-skewed, reversed-J-shaped, and J-shaped densities and increasing, unimodal, decreasing, reversed-J-shaped, and J-shaped hazard rates. We derive some mathematical properties of the proposed model. The model parameters were estimated using five estimation methods including the maximum likelihood, Anderson–Darling, least-squares, Cramér–von Mises, and weighted least-squares estimation methods. The performance of these estimation methods was assessed by a detailed simulation study. Furthermore, the flexibility of the introduced model was studied using an insurance real dataset, showing that the proposed model can be used to fit the insurance data as compared with twelve competing models.

scholarly journals A New Generalized Odd Gamma Uniform Distribution: Mathematical Properties, Application and Simulation

2021 ◽  
Vol 20 ◽  
pp. 135-146
Author(s):  
B. Hossieni ◽  
M. Afshari ◽  
M. Alizadeh ◽  
H. Karamikabir
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Mathematical Properties ◽  
Anderson Darling ◽  
Von Mises ◽  
High Degree

n many applied areas there is a clear need for the extended forms of the well-known distributions.The new distributions are more flexible to model real data that present a high degree of skewness and kurtosis, such that each one solves a particular part of the classical distribution problems. In this paper, a new two-parameter Generalized Odd Gamma distribution, called the (GOGaU) distribution, is introduced and the fitness capability of this model are investigated. Some structural properties of the new distribution are obtained. The different methods including: Maximum likelihood estimators, Bayesian estimators (posterior mean and maximum a posterior), least squares estimators, weighted least squares estimators, Cramér-von-Mises estimators, Anderson-Darling and right tailed Anderson-Darling estimators are discussed to estimate the model parameters. In order to perform the applications, the importance and flexibility of the new model are also illustrated empirically by means of two real data sets. For simulation Stan and JAGS software were utilized in which we have built the GOGaU JAGS module

Stein-rule estimation of coefficients for 18 eastern hardwood cubic volume equations

1986 ◽  
Vol 16 (2) ◽  
pp. 249-255 ◽  
Author(s):  
Edwin J. Green ◽  
William E. Strawderman
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Weighted Average ◽  
Total Sample ◽  
Ordinary Least Squares ◽  
Validation Data ◽  
Regression Parameters ◽  
Volume Equation ◽  
Mean Square Errors ◽  
Least Squares Estimates

A Stein-rule estimator, which shrinks least squares estimates of regression parameters toward their weighted average, was employed to estimate the coefficient in the constant form factor volume equation for 18 species simultaneously. The Stein-rule procedure was applied to ordinary least squares estimates and weighted least squares estimates. Simulation tests on independent validation data sets revealed that the Stein-rule estimates were biased, but predicted better than the corresponding least squares estimates. The Stein-rule procedures also yielded lower estimated mean square errors for the volume equation coefficient than the corresponding least squares procedure. Different methods of withdrawing sample data from the total sample available for each species revealed that the superiority of Stein-rule procedures over least squares decreased as the sample size increased and that the Stein-rule procedures were robust to unequal sample sizes, at least on the scale studied here.

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