scholarly journals The normal-tangent-G class of probabilistic distributions: properties and real data modellin

2020 ◽  
pp. 827-838
Author(s):  
Fábio Silveira ◽  
Frank Gomes-Silva ◽  
Cícero Brito ◽  
Moacyr Cunha-Filho ◽  
Jader Jale ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Distributions ◽  
Series Representation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Special Cases ◽  
Probability Density Function Pdf

This paper introduces a novel class of probability distributions called normal-tangent-G, whose submodels are parsi- monious and bring no additional parameters besides the baseline’s. We demonstrate that these submodels are iden- tifiable as long as the baseline is. We present some properties of the class, including the series representation of its probability density function (pdf) and two special cases. Monte Carlo simulations are carried out to study the behav- ior of the maximum likelihood estimates (MLEs) of the parameters for a particular submodel. We also perform an application of it to a real dataset to exemplify the modelling benefits of the class.

scholarly journals A New Generalized Family of Odd Lindley-G Distributions With Application

2019 ◽  
Vol 8 (6) ◽  
pp. 1
Author(s):  
Fastel Chipepa ◽  
Broderick O. Oluyede ◽  
Boikanyo Makubate
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Hazard Rate ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Lorenz Curves ◽  
New Family ◽  
Special Cases ◽  
Family Of Distributions

A new family of distributions, namely the Kumaraswamy Odd Lindley-G distribution is developed. The new density function can be expressed as a linear combination of exponentiated-G densities. Statistical properties of the new family including hazard rate and quantile functions, moments and incomplete moments, Bonferroni and Lorenz curves, distribution of order statistics and R´enyi entropy are derived. Some special cases are presented. We conduct some Monte Carlo simulations to examine the consistency of the maximum likelihood estimates. We provide an application of KOL-LLo distribution to a real data set.

scholarly journals Maximum Likelihood and Two-Step Estimation of an Ordered-Probit Selection Model

2007 ◽  
Vol 7 (2) ◽  
pp. 167-182 ◽  
Author(s):  
Richard Chiburis ◽  
Michael Lokshin
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Monte Carlo Simulations ◽  
Regression Model ◽  
Selection Rule ◽  
Ordered Probit ◽  
Maximum Likelihood Estimates ◽  
Full Information ◽  
Full Information Maximum Likelihood ◽  
Two Step Estimation

We discuss the estimation of a regression model with an ordered-probit selection rule. We have written a Stata command, oheckman, that computes two-step and full-information maximum-likelihood estimates of this model. Using Monte Carlo simulations, we compare the performances of these estimators under various conditions.

Half Logistic Odd Weibull-Topp-Leone-G Family of Distributions: Model, Properties and Applications

2020 ◽  
Vol 15 (4) ◽  
pp. 2481-2510
Author(s):  
Fastel Chipepa ◽  
Divine Wanduku ◽  
Broderick Olusegun Oluyede
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Statistical Properties ◽  
Maximum Likelihood Estimates ◽  
Special Cases ◽  
Family Of Distributions

A new flexible and versatile generalized family of distributions, namely, half logistic odd Weibull-Topp-Leone-G (HLOW-TL-G) distribution is presented. The distribution can be traced back to the exponentiated-G distribution. We derive the statistical properties of the proposed family of distributions. Maximum likelihood estimates of the HLOW-TL-G family of distributions are also presented. Five special cases of the proposed family are presented. A simulation study and real data applications on one of the special cases are also presented

scholarly journals A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 32-47
Author(s):  
Gauss Cordeiro ◽  
Maria de Lima ◽  
Edwin Ortega ◽  
Adriano Suzuki
Keyword(s):  
Maximum Likelihood ◽  
Regression Model ◽  
Real Data ◽  
Random Variable ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Poisson Random Variable ◽  
Fatigue Lifetime ◽  
Special Cases ◽  
New Distribution

We propose an extended fatigue lifetime model called the odd log-logistic Birnbaum–Saunders–Poisson distribution, which includes as special cases the Birnbaum–Saunders and odd log-logistic Birnbaum–Saunders distributions. We obtain some structural properties of the new distribution. We define a new extended regression model based on the logarithm of the odd log-logistic Birnbaum–Saunders–Poisson random variable. For censored data, we estimate the parameters of the regression model using maximum likelihood. We investigate the accuracy of the maximum likelihood estimates using Monte Carlo simulations. The importance of the proposed models, when compared to existing models, is illustrated by means of two real data sets.

scholarly journals The New Odd Lindley-G Power Series Class of Distributions: Theory, Properties and Applications

2021 ◽  
Vol 16 (3) ◽  
pp. 2819-2941
Author(s):  
Fastel Chipepa ◽  
Broderick Oluyede ◽  
Boikanyo Makubate
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Structural Properties ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Lorenz Curves ◽  
Proposed Model ◽  
Special Cases ◽  
Family Of Distributions

We propose a new generalized class of distributions called the odd Lindley-G Power Series (OL-GPS) family of distributions and a special class, namely, odd Lindley-Weibull power series (OL-WPS) family of distributions. We also derive the structural properties of the OL-GPS family of distributions including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates. Sub-models of the special cases were also obtained together with their structural properties. A simulation study to examine the consistency 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

Simulation of the Variability in Next-Generation Microelectronic Capacitors with Polycrystalline Dielectrics

2001 ◽  
Vol 688 ◽  
Author(s):  
Jesse L. Cousins ◽  
David E. Kotecki
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Area Distribution ◽  
The Mean ◽  
Polycrystalline Microstructure ◽  
Probability Density Function Pdf ◽  
Lognormal Probability

AbstractMonte Carlo simulations of capacitors with polycrystalline (Bax, Sr1−x)TiO3 (BST) dielectrics were performed. The variation in capacitors due to the polycrystalline microstructure of the dielectric was investigated, as well as the effects of varying the distribution of crystal sizes. When a lognormal probability density function (pdf) was used to approximate the crystal area pdf and the average number of crystals per capacitor was near 100, it was found that the minimum capacitance value was nearly independent of the standard deviation of crystal area distribution. Both the mean and maximum capacitance values were found to increase as the width of the standard deviation increased.

scholarly journals Normal-G Class of Probability Distributions: Properties and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1407 ◽  
Author(s):  
Fábio V. J. Silveira ◽  
Frank Gomes-Silva ◽  
Cícero C. R. Brito ◽  
Moacyr Cunha-Filho ◽  
Felipe R. S. Gusmão ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Probability Distributions ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Simulation Studies ◽  
Mathematical Properties ◽  
Parsimonious Models ◽  
The Moment ◽  
Probability Density Function Pdf

In this paper, we propose a novel class of probability distributions called Normal-G. It has the advantage of demanding no additional parameters besides those of the parent distribution, thereby providing parsimonious models. Furthermore, the class enjoys the property of identifiability whenever the baseline is identifiable. We present special Normal-G sub-models, which can fit asymmetrical data with either positive or negative skew. Other important mathematical properties are described, such as the series expansion of the probability density function (pdf), which is used to derive expressions for the moments and the moment generating function (mgf). We bring Monte Carlo simulation studies to investigate the behavior of the maximum likelihood estimates (MLEs) of two distributions generated by the class and we also present applications to real datasets to illustrate its usefulness.

scholarly journals Moments of Distance from a Vertex to a Uniformly Distributed Random Point within Arbitrary Triangles

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Hongjun Li ◽  
Xing Qiu
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Cumulative Distribution Function ◽  
Random Point ◽  
Cumulative Distribution ◽  
Computational Technique ◽  
Probability Density Function Pdf

We study the cumulative distribution function (CDF), probability density function (PDF), and moments of distance between a given vertex and a uniformly distributed random point within a triangle in this work. Based on a computational technique that helps us provide unified formulae of the CDF and PDF for this random distance then we compute its moments of arbitrary orders, based on which the variance and standard deviation can be easily derived. We conduct Monte Carlo simulations under various conditions to check the validity of our theoretical derivations. Our method can be adapted to study the random distances sampled from arbitrary polygons by decomposing them into triangles.

scholarly journals The New Odd Lindley-G Power Series Class of Distributions: Theory, Properties and Applications

2021 ◽  
Vol 16 (3) ◽  
pp. 2825-2949
Author(s):  
Fastel Chipepa ◽  
Broderick Oludeye ◽  
Boikanyo Makubate
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Structural Properties ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Lorenz Curves ◽  
Proposed Model ◽  
Special Cases ◽  
Family Of Distributions

We propose a new generalized class of distributions called the odd Lindley-G Power Series (OL-GPS) family of distributions and a special class, namely, odd Lindley-Weibull power series (OL-WPS) family of distributions. We also derive the structural properties of the OL-GPS family of distributions including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates. Sub-models of the special cases were also obtained together with their structural properties. A simulation study to examine the consistency 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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