A new family of polyno-expo-trigonometric distributions with applications

In this paper, a new family of polyno-expo-trigonometric distributions is presented and investigated. A special case using the Weibull distribution, with three parameters, is considered as statistical model for lifetime data. The estimation of the parameters is performed with the maximum likelihood method. A numerical simulation study verifies that the bias and the mean squared error of the maximum likelihood estimators tend to zero as the sample size is increased. Three real life datasets are then analyzed. We show that our model has a good fit in comparison to the other well-known powerful models in the literature.

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A New Family of Continuous Probability Distributions

Entropy ◽

10.3390/e23020194 ◽

2021 ◽

Vol 23 (2) ◽

pp. 194

Author(s):

M. El-Morshedy ◽

Fahad Sameer Alshammari ◽

Yasser S. Hamed ◽

Mohammed S. Eliwa ◽

Haitham M. Yousof

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Probability Distributions ◽

Real Life ◽

Likelihood Method ◽

Model Parameters ◽

Finite Sample ◽

Graphical Simulation ◽

New Family ◽

The One

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of “Farlie-Gumbel-Morgenstern copula”, “the modified Farlie-Gumbel-Morgenstern copula”, “the Clayton copula”, and “the Renyi’s entropy copula” are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

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A Comparative Study for Weighted Rayleigh Distribution

Journal of Reliability and Statistical Studies ◽

10.13052/jrss0974-8024.14112 ◽

2021 ◽

Author(s):

Sofi Mudasir Ahad ◽

Sheikh Parvaiz Ahmad ◽

Sheikh Aasimeh Rehman

Keyword(s):

Maximum Likelihood Method ◽

Mean Squared Error ◽

Real Life ◽

Rayleigh Distribution ◽

Likelihood Method ◽

Data Sets ◽

Posterior Distributions ◽

Bayes Estimators ◽

Squared Error ◽

Real Life Data

In this paper, Bayesian and non-Bayesian methods are used for parameter estimation of weighted Rayleigh (WR) distribution. Posterior distributions are derived under the assumption of informative and non-informative priors. The Bayes estimators and associated risks are obtained under different symmetric and asymmetric loss functions. Results are compared on the basis of posterior risk and mean square error using simulated and real life data sets. The study depicts that in order to estimate the scale parameter of the weighted Rayleigh distribution use of entropy loss function under Gumbel type II prior can be preferred. Also, Bayesian method of estimation having least values of mean squared error gives better results as compared to maximum likelihood method of estimation.

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Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics

Mathematical Problems in Engineering ◽

10.1155/2020/8974349 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17

Author(s):

Ghadah Alomani ◽

Refah Alotaibi ◽

Sanku Dey ◽

Mahendra Saha

Keyword(s):

Maximum Likelihood ◽

Confidence Intervals ◽

Maximum Likelihood Method ◽

Mean Squared Error ◽

Quality Characteristics ◽

Likelihood Method ◽

Squared Error ◽

Relative Coverage ◽

Anderson Darling ◽

Percentile Bootstrap

The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance. Usually, conventional PCIs perform well under normally distributed quality characteristics. However, when these PCIs are employed to evaluate nonnormally distributed process, they often provide inaccurate results. In this article, in order to estimate the PCI Spmk when the process follows power Lindley distribution, first, seven classical methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares methods of estimation, Cramèr–von Mises method of estimation, maximum product of spacings method of estimation, Anderson–Darling, and right-tail Anderson–Darling methods of estimation, are considered and the performance of these estimation methods based on their mean squared error is compared. Next, three bootstrap confidence intervals (BCIs) of the PCI Spmk, namely, standard bootstrap, percentile bootstrap, and bias-corrected percentile bootstrap, are considered and compared in terms of their average width, coverage probability, and relative coverage. Besides, a new cost-effective PCI, namely, Spmkc is introduced by incorporating tolerance cost function in the index Spmk. To evaluate the performance of the methods of estimation and BCIs, a simulation study is carried out. Simulation results showed that the maximum likelihood method of estimation performs better than their counterparts in terms of mean squared error, while bias-corrected percentile bootstrap provides smaller confidence length (width) and higher relative coverage than standard bootstrap and percentile bootstrap across sample sizes. Finally, two real data examples are provided to investigate the performance of the proposed procedures.

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The extended odd family of probability distributions with practice to a submodel

Filomat ◽

10.2298/fil1912855b ◽

2019 ◽

Vol 33 (12) ◽

pp. 3855-3867 ◽

Cited By ~ 2

Author(s):

Hassan Bakouch ◽

Christophe Chesneau ◽

Muhammad Khan

Keyword(s):

Heavy Tails ◽

Maximum Likelihood Method ◽

Probability Distributions ◽

Likelihood Method ◽

Tuning Parameter ◽

Data Sets ◽

New Family ◽

Rate Functions ◽

Special Case ◽

Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

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Best estimation for the Reliability of 2-parameter Weibull Distribution

Baghdad Science Journal ◽

10.21123/bsj.6.4.705-710 ◽

2009 ◽

Vol 6 (4) ◽

pp. 705-710

Author(s):

Baghdad Science Journal

Keyword(s):

Maximum Likelihood ◽

Weibull Distribution ◽

Mean Square Error ◽

Maximum Likelihood Method ◽

Likelihood Method ◽

Statistical Criterion ◽

Mean Square ◽

Simulation Process ◽

The Mean ◽

Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

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The Poisson Nadarajah–Haghighi Distribution: Properties and Applications to Lifetime Data

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539320500059 ◽

2019 ◽

Vol 27 (01) ◽

pp. 2050005

Author(s):

Muhammad Mansoor ◽

M. H. Tahir ◽

Aymaan Alzaatreh ◽

Gauss M. Cordeiro

Keyword(s):

Maximum Likelihood ◽

Censored Data ◽

Survival Data ◽

Maximum Likelihood Method ◽

Likelihood Estimation ◽

Real Data ◽

Likelihood Method ◽

Lifetime Data ◽

Monte Carlo Simulation Study ◽

Mathematical Properties

A new three-parameter compounded extended-exponential distribution “Poisson Nadarajah–Haghighi” is introduced and studied, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub-shaped failure rate. A comprehensive account of the mathematical properties of the model is presented. We discuss maximum likelihood estimation for complete and censored data. The suitability of the maximum likelihood method to estimate its parameters is assessed by a Monte Carlo simulation study. Four empirical illustrations of the new model are presented to real data and the results are quite satisfactory.

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Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Mathematics ◽

10.3390/math8030358 ◽

2020 ◽

Vol 8 (3) ◽

pp. 358 ◽

Cited By ~ 3

Author(s):

M. S. Eliwa ◽

Ziyad Ali Alhussain ◽

M. El-Morshedy

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Discrete Analogue ◽

Likelihood Method ◽

New Family ◽

Distributional Properties ◽

Reliability Characteristics ◽

Proposed Model ◽

The Family ◽

Family Of Distributions

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

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A New Ridge-Type Estimator for the Gamma Regression Model

Scientifica ◽

10.1155/2021/5545356 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Adewale F. Lukman ◽

Issam Dawoud ◽

B. M. Golam Kibria ◽

Zakariya Y. Algamal ◽

Benedicta Aladeitan

Keyword(s):

Biological Activity ◽

Regression Model ◽

Mean Squared Error ◽

Real Life ◽

Regression Parameter ◽

Likelihood Estimator ◽

Response Variable ◽

Explanatory Variables ◽

Squared Error ◽

The Mean

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

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A new estimator for the multicollinear Poisson regression model: simulation and application

Scientific Reports ◽

10.1038/s41598-021-82582-w ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Adewale F. Lukman ◽

Emmanuel Adewuyi ◽

Kristofer Månsson ◽

B. M. Golam Kibria

Keyword(s):

Regression Model ◽

Poisson Regression ◽

Mean Squared Error ◽

Model Simulation ◽

Real Life ◽

Poisson Regression Model ◽

Squared Error ◽

Damage Data ◽

The Mean ◽

Better Than

AbstractThe maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.

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Inverse Lomax-Exponentiated G (IL-EG) Family of Distributions: Properties and Applications

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2020/v9i430234 ◽

2020 ◽

pp. 48-64

Author(s):

Jamilu Yunusa Falgore ◽

Sani Ibrahim Doguwa

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Moment Generating Function ◽

Maximum Likelihood Estimates ◽

Likelihood Method ◽

Data Sets ◽

Baseline Model ◽

New Family ◽

Family Of Distributions ◽

Better Than

A new generator of continuous distributions called the Inverse Lomax-Exponentiated G family, which has three extra positive parameters is proposed. The structural properties of the new family that holds for any continuous baseline model including explicit density function expressions, moments, inequality measurements, moment generating function, reliability functions, Renyi and Shanon entropies, and distribution of order statistics are derived. A Monte Carlo simulation to test the efficiency of the maximum likelihood estimates is conducted. The application of the new sub-model to the two data sets using the maximum likelihood method indicates that the new model is better than the existing competitors.

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