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Full-Text Articles in Physical Sciences and Mathematics
(R2024) A New Weighted Poisson Distribution For Over- And Under-Dispersion Situations, Michel Koukouatikissa Diafouka, Gelin Chedly Louzayadio, Rodnellin Onéime Malouata
(R2024) A New Weighted Poisson Distribution For Over- And Under-Dispersion Situations, Michel Koukouatikissa Diafouka, Gelin Chedly Louzayadio, Rodnellin Onéime Malouata
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we propose a four-parameter weighted Poisson distribution that includes and generalizes the weighted Poisson distribution proposed by Castillo and Pérez-Casany and the Conway- Maxwell-Poisson distribution, as well as other well-known distributions. It is a distribution that is a member of the exponential family and is an exponential combination formulation between the weighted Poisson distribution proposed by Castillo and Pérez-Casany and the Conway-Maxwell- Poisson distribution. This new distribution with an additional parameter of dispersion is more flexible, and the Fisher dispersion index can be greater than, equal to, or less than one. This last property allows it to …
(R1239) A New Type Ii Half Logistic-G Family Of Distributions With Properties, Regression Models, System Reliability And Applications, Emrah Altun, Morad Alizadeh, Haitham M. Yousof, Mahdi Rasekhi, G. G. Hamedani
(R1239) A New Type Ii Half Logistic-G Family Of Distributions With Properties, Regression Models, System Reliability And Applications, Emrah Altun, Morad Alizadeh, Haitham M. Yousof, Mahdi Rasekhi, G. G. Hamedani
Applications and Applied Mathematics: An International Journal (AAM)
This study proposes a new family of distributions based on the half logistic distribution. With the new family, the baseline distributions gain flexibility through additional shape parameters. The important statistical properties of the proposed family are derived. A new generalization of the Weibull distribution is used to introduce a location-scale regression model for the censored response variable. The utility of the introduced models is demonstrated in survival analysis and estimation of the system reliability. Three data sets are analyzed. According to the empirical results, it is observed that the proposed family gives better results than other existing models.
A New Liu Type Of Estimator For The Restricted Sur Estimator, Kristofer Månsson, B. M. Golam Kibria, Ghazi Shukur
A New Liu Type Of Estimator For The Restricted Sur Estimator, Kristofer Månsson, B. M. Golam Kibria, Ghazi Shukur
Journal of Modern Applied Statistical Methods
A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity.
A Generalization Of The Weibull Distribution With Applications, Maalee Almheidat, Carl Lee, Felix Famoye
A Generalization Of The Weibull Distribution With Applications, Maalee Almheidat, Carl Lee, Felix Famoye
Journal of Modern Applied Statistical Methods
The Lomax-Weibull distribution, a generalization of the Weibull distribution, is characterized by four parameters that describe the shape and scale properties. The distribution is found to be unimodal or bimodal and it can be skewed to the right or left. Results for the non-central moments, limiting behavior, mean deviations, quantile function, and the mode(s) are obtained. The relationships between the parameters and the mean, variance, skewness, and kurtosis are provided. The method of maximum likelihood is proposed for estimating the distribution parameters. The applicability of this distribution to modeling real life data is illustrated by three examples and the results …
Measurement Error Estimation Methods In Survey Methodology, Alireza Zahedian, Roshanak A. Saba
Measurement Error Estimation Methods In Survey Methodology, Alireza Zahedian, Roshanak A. Saba
Applications and Applied Mathematics: An International Journal (AAM)
One of the most important topics that are discussed in survey methodology is the accuracy of statistics or survey errors that may occur in the parameters estimation process. In statistical literature, these errors are grouped into two main categories: sampling errors and non-sampling errors. Measurement error is one of the most important non-sampling errors. Since estimating of measurement error is more complex than other types of survey errors, much more research has been done on ways of preventing or dealing with this error. The main problem associated with measurement error is the difficulty to measure or estimate this error in …
A Note On Α-Curvature Of The Manifolds Of The Length-Biased Lognormal And Gamma Distributions In View Of Related Applications In Data Analysis, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
A Note On Α-Curvature Of The Manifolds Of The Length-Biased Lognormal And Gamma Distributions In View Of Related Applications In Data Analysis, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
Journal of Modern Applied Statistical Methods
The α-curvature tensors of the statistical manifolds of the length-biased versions of the log-normal and gamma distributions are derived and discussed. This study was designed to investigate observations related to the parameter estimation for the length-biased lognormal distribution as a model for the lengthbiased data from oil field exploration.
The Length-Biased Lognormal Distribution And Its Application In The Analysis Of Data From Oil Field Exploration Studies, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
The Length-Biased Lognormal Distribution And Its Application In The Analysis Of Data From Oil Field Exploration Studies, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
Journal of Modern Applied Statistical Methods
The length-biased version of the lognormal distribution and related estimation problems are considered and sized-biased data arising in the exploration of oil fields is analyzed. The properties of the estimators are studied using simulations and the use of sample mode as an estimate of the lognormal parameter is discussed.
Gamma-Pareto Distribution And Its Applications, Ayman Alzaatreh, Felix Famoye, Carl Lee
Gamma-Pareto Distribution And Its Applications, Ayman Alzaatreh, Felix Famoye, Carl Lee
Journal of Modern Applied Statistical Methods
A new distribution, the gamma-Pareto, is defined and studied and various properties of the distribution are obtained. Results for moments, limiting behavior and entropies are provided. The method of maximum likelihood is proposed for estimating the parameters and the distribution is applied to fit three real data sets.
New Approximate Bayesian Confidence Intervals For The Coefficient Of Variation Of A Gaussian Distribution, Vincent A. R. Camara
New Approximate Bayesian Confidence Intervals For The Coefficient Of Variation Of A Gaussian Distribution, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
Confidence intervals are constructed for the coefficient of variation of a Gaussian distribution. Considering the square error and the Higgins-Tsokos loss functions, approximate Bayesian models are derived and compared to a published classical model. The models are shown to have great coverage accuracy. The classical model does not always yield the best confidence intervals; the proposed models often perform better.
Estimation Of Parameters Of Johnson’S System Of Distributions, Florence George, K. M. Ramachandran
Estimation Of Parameters Of Johnson’S System Of Distributions, Florence George, K. M. Ramachandran
Journal of Modern Applied Statistical Methods
Fitting distributions to data has a long history and many different procedures have been advocated. Although models like normal, log-normal and gamma lead to a wide variety of distribution shapes, they do not provide the degree of generality that is frequently desirable (Hahn & Shapiro, 1967). To formally represent a set of data by an empirical distribution, Johnson (1949) derived a system of curves with the flexibility to cover a wide variety of shapes. Methods available to estimate the parameters of the Johnson distribution are discussed, and a new approach to estimate the four parameters of the Johnson family is …
Approximate Bayesian Confidence Intervals For The Mean Of A Gaussian Distribution Versus Bayesian Models, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Mean Of A Gaussian Distribution Versus Bayesian Models, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
This study obtained and compared confidence intervals for the mean of a Gaussian distribution. Considering the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the mean of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals were compared to a published Bayesian model. Whereas the published Bayesian method is sensitive to the choice of the hyper-parameters and does not always yield the best confidence intervals, it is shown that the proposed approximate Bayesian approach relies only on the observations and often performs better.
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of this article is to obtain and compare confidence intervals for the mean of an exponential distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for parameters of exponential population are derived. Using exponential data, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with Fisher Matrix bounds method. It is shown that the proposed approximate Bayesian approach relies only on the observations. The Fisher Matrix bounds method, that uses the z-table, does not always yield the best confidence intervals, and the proposed approach often performs better.
Bayesian Reliability Modeling Using Monte Carlo Integration, Vincent A. R. Camara, Chris P. Tsokos
Bayesian Reliability Modeling Using Monte Carlo Integration, Vincent A. R. Camara, Chris P. Tsokos
Journal of Modern Applied Statistical Methods
Bayesian Reliability Modeling Using Monte Carlo IntegrationThe aim of this article is to introduce the concept of Monte Carlo Integration in Bayesian estimation and Bayesian reliability analysis. Using the subject concept, approximate estimates of parameters and reliability functions are obtained for the three-parameter Weibull and the gamma failure models. Four different loss functions are used: square error, Higgins-Tsokos, Harris, and a logarithmic loss function proposed in this article. Relative efficiency is used to compare results obtained under the above mentioned loss functions.
Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of the present study is to obtain and compare confidence intervals for the variance of a Gaussian distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the variance of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with the well known classical method. The Bayesian approach relies only on the observations. It is shown that the proposed approximate Bayesian approach relies only on the observations. The classical method, that uses the Chi-square statistic, does …