scholarly journals STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE GENERALIZED RAYLEIGH DISTRIBUTION

2021 ◽  
pp. 1107
Author(s):  
Cenker Biçer ◽  
Hayrinisa D. Biçer ◽  
Mahmut Kara ◽  
Asuman Yılmaz
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Inference Problem ◽  
Geometric Process ◽  
Generalized Rayleigh Distribution ◽  
First Arrival ◽  
Modeling Behavior

In the present paper, statistical inference problem is considered for the geometric process (GP) by assuming the distribution of the first arrival time is generalized Rayleigh with the parameters $\alpha$ and $\lambda$. We use the maximum likelihood method for obtaining the ratio parameter of the GP and distributional parameters of the generalized Rayleigh distribution. By a series of Monte-Carlo simulations evaluated through the different samples of sizes small, moderate and large, we also compare the estimation performances of the maximum likelihood estimators with the other estimators available in the literature such as modified moment, modified L-moment, and modified least squares. Furthermore, we present two real-life dataset analyzes to show the modeling behavior of GP with generalized Rayleigh distribution.

scholarly journals Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 451
Author(s):  
Hayrinisa Demirci Biçer
Keyword(s):  
Statistical Inference ◽  
Arrival Time ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Arrival Times ◽  
Generalized Rayleigh Distribution ◽  
First Arrival ◽  
L Moments ◽  
Monotone Trend ◽  
First Arrival Time

In the modeling of successive arrival times with a monotone trend, the alpha-series process provides quite successful results. Both selecting the distribution of the first arrival time and making an optimal statistical inference play a crucial role in the modeling performance of the alpha-series process. In this study, when the distribution of the first arrival time is the generalized Rayleigh, the problem of statistical inference for the α , β , and λ parameters of the alpha-series process is considered. Further, in order to obtain optimal modeling performance from the mentioned alpha-series process, various estimators for the model parameters are obtained by employing different estimation methodologies such as maximum likelihood, modified maximum spacing, modified least-squares, modified moments, and modified L-moments. By a series of Monte Carlo simulations, the estimation efficiencies of the obtained estimators are evaluated through the different sample sizes. Finally, two real datasets are analyzed to illustrate the importance of modeling with the alpha-series process.

Statistical inference for Markov processes when the model is incorrect

1979 ◽  
Vol 11 (04) ◽  
pp. 737-749
Author(s):  
Robert V. Foutz ◽  
R. C. Srivastava
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Likelihood Ratio ◽  
Markov Processes ◽  
Transition Probability ◽  
Likelihood Ratio Statistic ◽  
Null Distribution ◽  
Transition Density ◽  
Likelihood Method ◽  
Incorrect Model

Statistical inference for Markov processes is commonly based on the maximum likelihood method of estimation and the likelihood ratio criterion for testing hypotheses. Construction of estimators and test statistics by these methods require that a model be chosen in the form of a family of transition density functions. In this paper, asymptotic properties of the maximum likelihood estimator and of the likelihood ratio statistic λ n are examined when the model chosen for their construction is incorrect—that is, when no density in the model is a density for the transition probability distribution of the Markov process. It is shown that if and λ n are constructed from a ‘regular’ incorrect model, then is consistent and asymptotically normally distributed and the asymptotic null distribution of −2 log λ n is that of a linear combination of independent chi-squared random variables. These results are applied to propose measures of the performance of the test based on λ n when the statistic is constructed from an incorrect model.

scholarly journals A New Family of Continuous Probability Distributions

Entropy ◽  
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.

scholarly journals Statistical Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2703
Author(s):  
Ke Wu ◽  
Liang Wang ◽  
Li Yan ◽  
Yuhlong Lio
Keyword(s):  
Statistical Inference ◽  
Information Matrix ◽  
Real Life ◽  
High Posterior Density ◽  
Rayleigh Distribution ◽  
Maximum Likelihood Estimates ◽  
Approximate Theory ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Right Censored Data

In this paper, statistical inference and prediction issue of left truncated and right censored dependent competing risk data are studied. When the latent lifetime is distributed by Marshall–Olkin bivariate Rayleigh distribution, the maximum likelihood estimates of unknown parameters are established, and corresponding approximate confidence intervals are also constructed by using a Fisher information matrix and asymptotic approximate theory. Furthermore, Bayesian estimates and associated high posterior density credible intervals of unknown parameters are provided based on general flexible priors. In addition, when there is an order restriction between unknown parameters, the point and interval estimates based on classical and Bayesian frameworks are discussed too. Besides, the prediction issue of a censored sample is addressed based on both likelihood and Bayesian methods. Finally, extensive simulation studies are conducted to investigate the performance of the proposed methods, and two real-life examples are presented for illustration purposes.

scholarly journals A New Kumaraswamy Generalized Family of Distributions with Properties, Applications and Bivariate Extension

2020 ◽  
Author(s):  
Muhammad H. Tahir ◽  
Muhammad Adnan Hussain ◽  
Gauss Cordeiro ◽  
Mahmoud El-Morshedy ◽  
Mohammed S. Eliwa
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Unit Interval ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
The Family ◽  
Family Of Distributions

For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions from a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de-Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for estimating the family parameters. We investigate the properties of one special model called a new Kumaraswamy-Weibull (NKwW) distribution. Parameter estimation is dealt and maximum likelihood estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of this distribution. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull, exponentiated-Weibull and Weibull distributions when applied to these data sets. The bivariate extension of the family is proposed and the estimation of parameters is given. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

scholarly journals A Comparative Study for Weighted Rayleigh Distribution

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.

scholarly journals A Continuous Poisson-Rayleigh Distribution: Its Properties and Applications

2021 ◽  
pp. 69-84
Author(s):  
Abraham Iorkaa Asongo ◽  
Innocent Boyle Eraikhuemen ◽  
Emmanuel Remi Omoboriowo ◽  
Isa Abubakar Ibrahim
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Method Of Maximum Likelihood ◽  
New Distribution

This article proposed a Poisson based continuous probability distribution called Poisson-Rayleigh distribution. Some properties of the new distribution such as quantile and reliability functions and other useful measures were obtained. The model parameters were estimated using the method of maximum likelihood. The usefulness of the new distribution was proven empirically using real life datasets.

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