Erlang mixture distribution with application on COVID-19 cases in egypt

2021 ◽  
pp. 2150015
Author(s):  
M. M. E. Abd El-Monsef
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Finite Mixture ◽  
Erlang Distribution ◽  
Parameter Estimates ◽  
Proposed Model ◽  
Shape Characteristics ◽  
Erlang Distributions ◽  
Special Case

In this paper, a finite mixture of m-Erlang distributions is proposed. Different moments, shape characteristics and parameter estimates of the proposed model are also provided. The proposed mixture has the property that it has a bounded hazard function. A special case of the mixed Erlang distribution is introduced and discussed. In addition, a predictive technique is introduced to estimate the needed number of mixture components to fit a certain data. A real data concerning the confirmed COVID-19 cases in Egypt is introduced to utilize the predictive estimation technique. Two more real datasets are used to examine the flexibility of the proposed model.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

2019 ◽  
Author(s):  
Leili Tapak ◽  
Omid Hamidi ◽  
Majid Sadeghifar ◽  
Hassan Doosti ◽  
Ghobad Moradi
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Real Data ◽  
P Value ◽  
Parameter Estimates ◽  
Beta Regression ◽  
Rate Data ◽  
Data Set ◽  
Proposed Model ◽  
Beta Regression Model

Abstract Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

scholarly journals Estimating of Survival Function under Type One Censoring Sample for Mixture Distribution

2020 ◽  
Vol 33 (4) ◽  
pp. 102
Author(s):  
Qesma S. Abadi ◽  
Iden H. AL-Kanani
Keyword(s):  
Probability Density Function ◽  
Censored Data ◽  
Hazard Function ◽  
Shape Parameter ◽  
Survival Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Likelihood Estimator ◽  
Censored Sample ◽  
Newton Raphson

In this article, it is interesting to estimate and derive the three parameters which contain two scales parameters and one shape parameter of a new mixture distribution for the singly type one censored data which is the branch of right censored sample. Then to define some special mathematical and statistical properties for this new mixture distribution which is considered one of the continuous distributions characterized by its flexibility. Next,  using maximum likelihood estimator method for singly type one censored data based on the Newton-Raphson matrix procedure to find and estimate values of these three parameter by utilizing the real data taken from the National Center for Research and Treatment of Hematology/University of Mustansiriyah for leukemia diseases. After that we find and derive the estimate of probability density function, estimate survival function and finally estimate the hazard function. 

scholarly journals Marshall-Olkin Alpha Power Rayleigh Distribution: Properties, Characterizations, Estimation and Engineering applications

2021 ◽  
pp. 745-760
Author(s):  
Ehab Mohamed Almetwally ◽  
Ahmed Z. Afify ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Alpha Power ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Estimation ◽  
Proposed Model

In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.

scholarly journals The The Topp Leone-G Power Series Class of Distributions with Applications

2021 ◽  
pp. 827-846
Author(s):  
Fastel Chipepa ◽  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Kethamile Rannona
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Poisson Distribution ◽  
Simulation Study ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
New Class ◽  
Proposed Model ◽  
Special Case

We present a new class of distributions called the Topp-Leone-G Power Series (TL-GPS) class of distributions. This model is obtained by compounding the Topp-Leone-G distribution with the power series distribution. Statistical prop- erties of the TL-GPS class of distributions are obtained. Maximum likelihood estimates for the proposed model were obtained. A simulation study is carried out for the special case of Topp-Leone Log-Logistic Poisson distribution to assess the performance of the maximum likelihood estimates. Finally, we apply Topp-Leone-log-logistic Poisson distribution to real data sets to illustrate the usefulness and applicability of the proposed class of distributions.

scholarly journals A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 929
Author(s):  
Mohammad Reza Mahmoudi ◽  
Mohsen Maleki ◽  
Dumitru Baleanu ◽  
Vu-Thanh Nguyen ◽  
Kim-Hung Pho
Keyword(s):  
Bayesian Analysis ◽  
Heavy Tails ◽  
Linear Time ◽  
Real Data ◽  
Finite Mixture ◽  
Stochastic Representation ◽  
Bayesian Approaches ◽  
Proposed Model ◽  
Heavy Tailed ◽  
Informative Prior Distributions

In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN–MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models.

Weibull mixture regression for marginal inference in zero-heavy continuous outcomes

2015 ◽  
Vol 26 (3) ◽  
pp. 1476-1499 ◽  
Author(s):  
Mulugeta Gebregziabher ◽  
Delia Voronca ◽  
Abeba Teklehaimanot ◽  
Elizabeth J Santa Ana
Keyword(s):  
Mean Squared Error ◽  
Controlled Trial ◽  
Real Data ◽  
Parameter Estimates ◽  
Addictive Disorders ◽  
Mixture Regression ◽  
Finite Samples ◽  
Proposed Model ◽  
Continuous Outcomes ◽  
Log Normal

Continuous outcomes with preponderance of zero values are ubiquitous in data that arise from biomedical studies, for example studies of addictive disorders. This is known to lead to violation of standard assumptions in parametric inference and enhances the risk of misleading conclusions unless managed properly. Two-part models are commonly used to deal with this problem. However, standard two-part models have limitations with respect to obtaining parameter estimates that have marginal interpretation of covariate effects which are important in many biomedical applications. Recently marginalized two-part models are proposed but their development is limited to log-normal and log-skew-normal distributions. Thus, in this paper, we propose a finite mixture approach, with Weibull mixture regression as a special case, to deal with the problem. We use extensive simulation study to assess the performance of the proposed model in finite samples and to make comparisons with other family of models via statistical information and mean squared error criteria. We demonstrate its application on real data from a randomized controlled trial of addictive disorders. Our results show that a two-component Weibull mixture model is preferred for modeling zero-heavy continuous data when the non-zero part are simulated from Weibull or similar distributions such as Gamma or truncated Gauss.

scholarly journals Generating New Flexible Lifetime Class of Distributions Based on Competing Risks and Frailty Models

2021 ◽  
pp. 1-19
Author(s):  
M. M. E. Abd El-Monsef ◽  
M. M. El-Awady
Keyword(s):  
Competing Risks ◽  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Lifetime Distribution ◽  
Frailty Models ◽  
Estimation Technique ◽  
Data Set ◽  
Egg Distribution ◽  
Proposed Model

New classes of continuous distributions have been generated, in the last decad, based on a compounding procedure arises on a latent competing risks problem. This procedure assumes the homogeneity between the population individuals. In this paper, a new lifetime distribution is generated, assuming the heterogeneity at both population and individual levels, called Extended Gamma Gompertz (EGG) distribution. This distribution shows very desirable exibility of its hazard function. Some properties of the proposed distribution are given. Maximum likelihood estimation technique is used to estimate the parameters. A simulation study is performed to examine the performance of the proposed model. Finally, application to a real data set is given to exemplify the utility of the EGG distribution.

scholarly journals Beta Exponentiated Modified Weibull Distribution: Properties and Application

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 781 ◽  
Author(s):  
Mirza Naveed Shahzad ◽  
Ehsan Ullah ◽  
Abid Hussanan
Keyword(s):  
Weibull Distribution ◽  
Reliability Analysis ◽  
Numerical Study ◽  
Real Data ◽  
Estimation Methods ◽  
Lifetime Distributions ◽  
Modified Weibull Distribution ◽  
Proposed Model ◽  
Modified Weibull ◽  
Special Case

One of the most prominent statistical distributions is the Weibull distribution. The recent modifications in this distribution have enhanced its application but only in specific fields. To introduce a more generalized Weibull distribution, in this work beta exponentiated modified Weibull distribution is established. This distribution consolidate the exponential, skewed and symmetric shapes into one density. The proposed distribution also contains nineteen lifetime distributions as a special case, which shows the flexibility of the distribution. The statistical properties of the proposed model are derived and discussed, including reliability analysis and order statistics. The hazard function of the proposed distribution can have a unimodal, decreasing, bathtub, upside-down bathtub, and increasing shape that make it effective in reliability analysis. The parameters of the proposed model are evaluated by maximum likelihood and least squares estimation methods. The significance of the beta exponentiated modified Weibull distribution for modeling is illustrated by the study of real data. The numerical study indicates that the new proposed distribution gives better results than other comparable distributions.

scholarly journals A New Class of Generalized Weibull-G Family of Distributions: Theory, Properties and Applications

2018 ◽  
Vol 8 (1) ◽  
pp. 73
Author(s):  
Baitshephi Mashabe ◽  
Broderick O. Oluyede ◽  
Adeniyi F. Fagbamigbe ◽  
Boikanyo Makubate ◽  
Syamala Krishnannair
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Mean Square ◽  
Conditional Moments ◽  
New Class ◽  
Proposed Model ◽  
Family Of Distributions

We propose a generalized class of distributions called the Webull-G Power Series (WGPS) family of distributions and its sub-model Weibull-G logarithmic (WGL) distributions. Structural properties of the WGPS family of distributions and its sub-model WGL distribution including hazard function, moments, conditional moments, order statistics, R&acute;enyi entropy and maximum likelihood estimates are derived. A simulation study to examine the bias, mean square error of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed model.

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