scholarly journals A Novel Chen Extension: Theory, Characterizations and Different Estimation Methods

2021 ◽  
Vol 2 ◽  
pp. 1
Author(s):  
Haitham M. Yousof ◽  
Mustafa C. Korkmaz ◽  
G.G. Hamedani ◽  
Mohamed Ibrahim
Keyword(s):  
Numerical Analysis ◽  
Maximum Likelihood ◽  
Weighted Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Simulation Studies ◽  
Data Set ◽  
Anderson Darling ◽  
Mean Variance ◽  
Skewness And Kurtosis

In this work, we derive a novel extension of Chen distribution. Some statistical properties of the new model are derived. Numerical analysis for mean, variance, skewness and kurtosis is presented. Some characterizations of the proposed distribution are presented. Different classical estimation methods under uncensored schemes such as the maximum likelihood, Anderson-Darling, weighted least squares and right-tail Anderson–Darling methods are considered. Simulation studies are performed in order to compare and assess the above-mentioned estimation methods. For comparing the applicability of the four classical methods, two application to real data set are analyzed.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

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.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

scholarly journals A Damaged Generalised Poisson Model and its Application to Reported and Unreported Accident Counts

2006 ◽  
Vol 36 (02) ◽  
pp. 463-487
Author(s):  
David P.M. Scollnik
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Poisson Model ◽  
Real Data ◽  
Estimation Methods ◽  
Actual Number ◽  
Future Period ◽  
Large Hospital ◽  
Data Set ◽  
Current Period

This paper investigates some models in which non-negative observations from a Poisson or generalised Poisson distribution are possibly damaged according to a binomial or quasi-binomial law. The latter case is appropriate when the observations are over-dispersed. Although the extent of the damage is not known, it is assumed that the event of whether or not damage occurred is discernible. The models are particularly suited for certain applications involving accident counts when evidence of certain accidents may be observed even though the accidents themselves may go unreported. Given the number of observed accidents and knowledge as to whether or not some additional accidents have gone unreported, these models may be used to make inferences concerning the actual number of unreported and total number of accidents in the current period, and the numbers of reported, unreported, and/or total accidents in a future period. The models are applied to a real data set giving reported and unreported patient accidents in a large hospital. Both maximum likelihood and Bayesian estimation methods are presented and discussed.

scholarly journals Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Samane Nematolahi ◽  
Sahar Nazari ◽  
Zahra Shayan ◽  
Seyyed Mohammad Taghi Ayatollahi ◽  
Ali Amanati
Keyword(s):  
Sampling Design ◽  
Ordered Set ◽  
Real Data ◽  
Estimation Methods ◽  
Simple Random Sample ◽  
Simulation Studies ◽  
Data Set ◽  
Kaplan Meier ◽  
Exact Measurement ◽  
General Estimation

This study presents a novel methodology to investigate the nonparametric estimation of a survival probability under random censoring time using the ranked observations from a Partially Rank-Ordered Set (PROS) sampling design and employs it in a hematological disorder study. The PROS sampling design has numerous applications in medicine, social sciences and ecology where the exact measurement of the sampling units is costly; however, sampling units can be ordered by using judgment ranking or available concomitant information. The general estimation methods are not directly applicable to the case where samples are from rank-based sampling designs, because the sampling units do not meet the identically distributed assumption. We derive asymptotic distribution of a Kaplan-Meier (KM) estimator under PROS sampling design. Finally, we compare the performance of the suggested estimators via several simulation studies and apply the proposed methods to a real data set. The results show that the proposed estimator under rank-based sampling designs outperforms its counterpart in a simple random sample (SRS).

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 A Damaged Generalised Poisson Model and its Application to Reported and Unreported Accident Counts

2006 ◽  
Vol 36 (2) ◽  
pp. 463-487
Author(s):  
David P.M. Scollnik
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Poisson Model ◽  
Real Data ◽  
Estimation Methods ◽  
Actual Number ◽  
Future Period ◽  
Large Hospital ◽  
Data Set ◽  
Current Period

This paper investigates some models in which non-negative observations from a Poisson or generalised Poisson distribution are possibly damaged according to a binomial or quasi-binomial law. The latter case is appropriate when the observations are over-dispersed. Although the extent of the damage is not known, it is assumed that the event of whether or not damage occurred is discernible. The models are particularly suited for certain applications involving accident counts when evidence of certain accidents may be observed even though the accidents themselves may go unreported. Given the number of observed accidents and knowledge as to whether or not some additional accidents have gone unreported, these models may be used to make inferences concerning the actual number of unreported and total number of accidents in the current period, and the numbers of reported, unreported, and/or total accidents in a future period. The models are applied to a real data set giving reported and unreported patient accidents in a large hospital. Both maximum likelihood and Bayesian estimation methods are presented and discussed.

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 A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 339 ◽  
Author(s):  
Mustapha Muhammad ◽  
Lixia Liu
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Real Data ◽  
Strength Parameter ◽  
Logistic Distribution ◽  
Strength Analysis ◽  
Model Parameters ◽  
Simulation Studies ◽  
Data Set ◽  
Leibler Divergence

In this paper, we introduced a new three-parameter probability model called Poisson generalized half logistic (PoiGHL). The new model possesses an increasing, decreasing, unimodal and bathtub failure rates depending on the parameters. The relationship of PoiGHL with the exponentiated Weibull Poisson (EWP), Poisson exponentiated Erlang-truncated exponential (PEETE), and Poisson generalized Gompertz (PGG) model is discussed. We also characterized the PoiGHL sub model, i.e the half logistic Poisson (HLP), based on certain functions of a random variable by truncated moments. Several mathematical and statistical properties of the PoiGHL are investigated such as moments, mean deviations, Bonferroni and Lorenz curves, order statistics, Shannon and Renyi entropy, Kullback-Leibler divergence, moments of residual life, and probability weighted moments. Estimation of the model parameters was achieved by maximum likelihood technique and assessed by simulation studies. The stress-strength analysis was discussed in detail based on maximum likelihood estimation (MLE), we derived the asymptotic confidence interval of R = P ( X 1 < X 2 ) based on the MLEs, and examine by simulation studies. In three applications to real data set PoiGHL provided better fit and outperform some other popular distributions. In the stress-strength parameter estimation PoiGHL model illustrated as a reliable choice in reliability analysis as shown using two real data set.

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