scholarly journals Statistical Inference of Sine Inverse Rayleigh Distribution

2022 ◽  
Vol 41 (1) ◽  
pp. 405-414
Author(s):  
Abdullah ◽  
Ali H. Ahmadini
Keyword(s):  
Statistical Inference ◽  
Rayleigh Distribution

scholarly journals Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 449 ◽  
Author(s):  
Abdullah M. Almarashi ◽  
Majdah M. Badr ◽  
Mohammed Elgarhy ◽  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Statistical Inference ◽  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Linear Representation ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
New Model ◽  
Entropy Measures ◽  
Lifetime Studies

The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.

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 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.

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.

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