New Bivariate Pareto Type II Models

Pareto type II distribution has been studied from many statisticians due to its important role in reliability modelling and lifetime testing. In this article, we introduce two bivariate Pareto Type II distributions; one is derived from copula and the other is based on mixture and copula. Parameter Estimates of the proposed distribution are obtained using the maximum likelihood method. The performance of the proposed bivariate distributions is examined using a simulation study. Finally, we analyze one data set under the proposed distributions to illustrate their flexibility for real-life applications.

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The shifted Gompertz-G family of distributions: Properties and applications

Mathematica Slovaca ◽

10.1515/ms-2021-0053 ◽

2021 ◽

Vol 71 (5) ◽

pp. 1291-1308

Author(s):

Joseph Thomas Eghwerido ◽

Friday Ikechukwu Agu

Keyword(s):

Goodness Of Fit ◽

Maximum Likelihood Method ◽

Real Life ◽

Likelihood Method ◽

Test Statistic ◽

Data Set ◽

Monte Carlo Simulation Study ◽

Proposed Model ◽

Left And Right ◽

Mean Variance

Abstract This article proposes a class of generator for classical statistical distribution called the shifted Gompertz-G (SHIGO-G) distribution for generating new continuous distributions. Special models of the proposed model were examined together with some of its statistical properties in closed form which makes it tractable for censored data. Its major properties include heavy tail, approximately symmetric, left and right skewed with a combination of exponential and a reverted Gumbel distributions called the Gompertz. The bivariate SHIGO-G is introduced. The parameters estimate of the proposed model was obtained by maximum likelihood method. A Monte Carlo simulation study was employed to investigate the performance of the estimators of the proposed model mean, variance, bias and mean square error. A two real life illustration was used to examine the empirical goodness-of-fit of the test statistic of the proposed model. The results of the real life applications show that the SHIGO-G model provides a better fit for the data set used.

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On the Omega Distribution: Some Properties and Estimation

Mathematics ◽

10.3390/math9060656 ◽

2021 ◽

Vol 9 (6) ◽

pp. 656

Author(s):

Abdelaziz Alsubie ◽

Zuber Akhter ◽

Haseeb Athar ◽

Mahfooz Alam ◽

Abd EL-Baset A. Ahmad ◽

...

Keyword(s):

Maximum Likelihood ◽

Order Statistics ◽

Maximum Likelihood Method ◽

Real Data ◽

Likelihood Method ◽

Type Ii ◽

Data Set ◽

Simulation Results ◽

Censoring Scheme ◽

Single And Product Moments

We obtain explicit expressions for single and product moments of the order statistics of an omega distribution. We also discuss seven methods to estimate the omega parameters. Various simulation results are performed to compare the performance of the proposed estimators. Furthermore, the maximum likelihood method is adopted to estimate the omega parameters under the type II censoring scheme. The usefulness of the omega distribution is proven using a real data set.

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

Mathematics ◽

10.3390/math8111989 ◽

2020 ◽

Vol 8 (11) ◽

pp. 1989

Author(s):

Muhammad H. Tahir ◽

Muhammad Adnan Hussain ◽

Gauss M. Cordeiro ◽

M. El-Morshedy ◽

M. S. Eliwa

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Real Life ◽

Unit Interval ◽

Likelihood Method ◽

Data Sets ◽

Data Set ◽

Life Data ◽

Real Life Data ◽

Family Of Distributions

For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through 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 the estimation of G-family parameters. We investigate the properties of one special model called the new Kumaraswamy-Weibull (NKwW) distribution. Parameters of NKwW model are estimated by using maximum likelihood method, and the performance of these estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of the proposed model. 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 and exponentiated-Weibull distributions when applied to these data sets. The bivariate extension of the family is also proposed, and the estimation of parameters is dealt. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

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The Discrete Type-II Half-Logistic Exponential Distribution with Applications to COVID-19 Data

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v17i4.3772 ◽

2021 ◽

pp. 921-932

Author(s):

Muhammad Ahsan ul Haq ◽

Ayesha Babar ◽

Sharqa Hashmi ◽

Abdulaziz S. Alghamdi ◽

Ahmed Z. Afify

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Method ◽

Real Life ◽

Discrete Models ◽

Likelihood Method ◽

Model Parameters ◽

Data Sets ◽

Type Ii ◽

Two Parameter ◽

Discrete Type

We propose a new two-parameter discrete model, called discrete Type-II half-logistics exponential (DTIIHLE) distribution using the survival discretization approach. The DTIIHLE distribution can be utilized to model COVID-19 data. The model parameters are estimated using the maximum likelihood method. A simulation study is conducted to evaluate the performance of the maximum likelihood estimators. The usefulness of the proposed distribution is evaluated using two real-life COVID-19 data sets. The DTIIHLE distribution provides a superior fit to COVID-19 data as compared with competitive discrete models including the discrete-Pareto, discrete Burr-XII, discrete log-logistic, discrete-Lindley, discrete-Rayleigh, discrete inverse-Rayleigh, and natural discrete-Lindley.

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The co-responsibility of mass and environment in the formation of lenticular galaxies

Proceedings of the International Astronomical Union ◽

10.1017/s1743921320001908 ◽

2020 ◽

Vol 15 (S359) ◽

pp. 173-174

Author(s):

A. Cortesi ◽

L. Coccato ◽

M. L. Buzzo ◽

K. Menéndez-Delmestre ◽

T. Goncalves ◽

...

Keyword(s):

Active Galactic Nuclei ◽

Maximum Likelihood Method ◽

Spiral Galaxies ◽

Galactic Nuclei ◽

Rotation Velocity ◽

Elliptical Galaxies ◽

Likelihood Method ◽

Data Set ◽

Lenticular Galaxies ◽

Galaxies Kinematics

AbstractWe present the latest data release of the Planetary Nebulae Spectrograph Survey (PNS) of ten lenticular galaxies and two spiral galaxies. With this data set we are able to recover the galaxies’ kinematics out to several effective radii. We use a maximum likelihood method to decompose the disk and spheroid kinematics and we compare it with the kinematics of spiral and elliptical galaxies. We build the Tully- Fisher (TF) relation for these galaxies and we compare with data from the literature and simulations. We find that the disks of lenticular galaxies are hotter than the disks of spiral galaxies at low redshifts, but still dominated by rotation velocity. The mechanism responsible for the formation of these lenticular galaxies is neither major mergers, nor a gentle quenching driven by stripping or Active Galactic Nuclei (AGN) feedback.

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Efficient Maximum-Likelihood Inference For The Isolation-With-Initial-Migration Model With Potentially Asymmetric Gene Flow

10.1101/052894 ◽

2016 ◽

Author(s):

Rui J. Costa ◽

Hilde Wilkinson-Herbots

Keyword(s):

Gene Flow ◽

Maximum Likelihood ◽

Dna Sequences ◽

Computing Time ◽

Likelihood Method ◽

Ancestral Population ◽

Parameter Estimates ◽

Fast Method ◽

Data Set ◽

Im Model

AbstractThe isolation-with-migration (IM) model is commonly used to make inferences about gene flow during speciation, using polymorphism data. However, Becquet and Przeworski (2009) report that the parameter estimates obtained by fitting the IM model are very sensitive to the model's assumptions (including the assumption of constant gene flow until the present). This paper is concerned with the isolation-with-initial-migration (IIM) model of Wilkinson-Herbots (2012), which drops precisely this assumption. In the IIM model, one ancestral population divides into two descendant subpopulations, between which there is an initial period of gene flow and a subsequent period of isolation. We derive a very fast method of fitting an extended version of the IIM model, which also allows for asymmetric gene flow and unequal population sizes. This is a maximum-likelihood method, applicable to data on the number of segregating sites between pairs of DNA sequences from a large number of independent loci. In addition to obtaining parameter estimates, our method can also be used to distinguish between alternative models representing different evolutionary scenarios, by means of likelihood ratio tests. We illustrate the procedure on pairs of Drosophila sequences from approximately 30,000 loci. The computing time needed to fit the most complex version of the model to this data set is only a couple of minutes. The R code to fit the IIM model can be found in the supplementary files of this paper.

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Probabilistic Approach to the Assessment of the Depth of Soil Freezing

Proceedings of 13th Baltic Sea Geotechnical Conference ◽

10.3846/13bsgc.2016.013 ◽

2016 ◽

Author(s):

Jerzy Antoni Żurański ◽

Andrzej Sobolewski

Keyword(s):

Soil Structure ◽

Maximum Likelihood Method ◽

Probabilistic Method ◽

Probabilistic Approach ◽

Climatic Conditions ◽

The Other ◽

Soil Freezing ◽

Likelihood Method ◽

Freezing Depth ◽

Characteristic Values

The paper deals with the probabilistic method of the assessment of the depth of soil freezing. Annual (winter) maxima of the position of the zero centigrade temperature measured in the soil were approximated by Gumbel probability distribution. Its parameters were estimated using maximum likelihood method. Results received on the base of data from 2 meteorological stations and 30 years of observations, called as characteristic values of 50-year return period, refelect the influence of the climatic conditions on the freezing depth. On the other hand the soil structure and its conditions also play an important role in freezing. Nowadays they may be taken into account using correction coefficients. It is concluded that this methods is more precise than a method using so called air freezing index. Received results are not the same as given in the old Polish Standard. New analysis is currently being done.

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Extended Odd Fréchet-G Family of Distributions

Journal of Probability and Statistics ◽

10.1155/2018/2931326 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 6

Author(s):

Suleman Nasiru

Keyword(s):

Maximum Likelihood Method ◽

Real Data ◽

Likelihood Method ◽

Data Sets ◽

Data Set ◽

New Class ◽

New Family ◽

Rate Functions ◽

The Given ◽

Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

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Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data

Mathematics ◽

10.3390/math8061000 ◽

2020 ◽

Vol 8 (6) ◽

pp. 1000 ◽

Cited By ~ 5

Author(s):

Luis Sánchez ◽

Víctor Leiva ◽

Manuel Galea ◽

Helton Saulo

Keyword(s):

Quantile Regression ◽

Spatial Data ◽

Spatial Model ◽

Regression Models ◽

Maximum Likelihood Method ◽

Marginal Distribution ◽

Likelihood Method ◽

Model Parameters ◽

Data Set ◽

Quantile Regression Model

In the present paper, a novel spatial quantile regression model based on the Birnbaum–Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum–Saunders distribution, where one of its parameters is associated with the quantile of the respective marginal distribution, is established. The model parameters are estimated by the maximum likelihood method. Finally, a data set is applied for illustrating the formulated model.

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Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data

Advances in Mathematical Physics ◽

10.1155/2020/2193787 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Maha A. Aldahlan

Keyword(s):

Maximum Likelihood Method ◽

Real Life ◽

Quantile Function ◽

Moment Generating Function ◽

Likelihood Method ◽

Logistic Distribution ◽

Model Parameters ◽

Alpha Power ◽

New Model ◽

Mathematical Properties

In this paper, a new three-parameter lifetime distribution is introduced; the new model is a generalization of the log-logistic (LL) model, and it is called the alpha power transformed log-logistic (APTLL) distribution. The APTLL distribution is more flexible than some generalizations of log-logistic distribution. We derived some mathematical properties including moments, moment-generating function, quantile function, Rényi entropy, and order statistics of the new model. The model parameters are estimated using maximum likelihood method of estimation. The simulation study is performed to investigate the effectiveness of the estimates. Finally, we used one real-life dataset to show the flexibility of the APTLL distribution.

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