scholarly journals Alpha Power Transformed Extended Bur II Distribution: Properties and Applications

2020 ◽  
pp. 50-63
Author(s):  
A. A. Ogunde ◽  
B. Ajayi ◽  
D. O. Omosigho
Keyword(s):  
Estimation Method ◽  
Likelihood Estimation ◽  
Moment Generating Function ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Real World Data ◽  
Mathematical Properties ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This paper presents a new generalization of the extended Bur II distribution. We redefined the Bur II distribution using the Alpha Power Transformation (APT) to obtain a new distribution called the Alpha Power Transformed Extended Bur II distribution. We derived several mathematical properties for the new model which includes moments, moment generating function, order statistics, entropy etc. and used a maximum likelihood estimation method to obtain the parameters of the distribution. Two real-world data sets were used for applications in order to illustrate the usefulness of the new distribution.

scholarly journals The Zubair-dagum Distribution

2021 ◽  
pp. 25-35
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Dagum Distribution ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.

scholarly journals The Modified Kumaraswamy Weibull Distribution: Properties and Applications in Reliability and Engineering Sciences

2020 ◽  
pp. 433-446
Author(s):  
M. E. Mead ◽  
Ahmed Afify ◽  
Nadeem Shafique Butt
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Hazard Rates ◽  
Alpha Power ◽  
Mathematical Properties ◽  
Engineering Sciences ◽  
Maximum Likelihood Estimation Method

We introduce the Kumaraswamy alpha power-G (KAP-G) family which extends the alpha power family (Mahdavi and Kundu, 2017) and some other families. We consider the Weibull as baseline for the KAP family and generate Kumaraswamy alpha power Weibull distribution which has right-skewed, left-skewed, symmetrical, and reversed-J shaped densities, and decreasing, increasing, bathtub, upside-down bathtub, increasing-decreasing–increasing, J shaped and reversed-J shaped hazard rates. The proposed distribution can model non-monotone  and monotone failure rates which are quite common in engineering and reliability studies. Some basic mathematical properties of the new model are derived. The maximum likelihood estimation method is used to evaluate the parameters and the observed information matrix is determined. The performance and flexibility of the proposed family is illustrated via two real data applications.

scholarly journals The Weibull Logistic-exponential Distribution: Its Properties and Applications

2020 ◽  
pp. 197-216
Author(s):  
I. U. Akata ◽  
J. E. Osemwenkhae
Keyword(s):  
Exponential Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Lifetime Data ◽  
Data Set ◽  
Lifetime Distributions ◽  
Mathematical Properties ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution ◽  
Generalized Distribution

In this paper, a new generalized distribution known as Weibull Logistic-Exponential Distribution (WLED) is proposed using the T-R{Y} framework. Several mathematical properties of this new distribution are studied. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution. Finally, an application of the proposed distribution to a real lifetime data set is presented and its fit was compared with the fit obtained by some comparable lifetime distributions.

scholarly journals The Characterization of the Cubic Rank Inverse Weibull Distribution

2020 ◽  
pp. 20-33 ◽  
Author(s):  
Ogunde Adebisi Ade ◽  
Chukwu Angela Unna ◽  
Agwuegbo Samuel Obi-Nnamd
Keyword(s):  
Weibull Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Moment Generating Function ◽  
Data Set ◽  
Inverse Weibull Distribution ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This work provides a new statistical distribution named Cubic rank transmuted Inverse Weibull distribution which was developed using the cubic transmutation map. Various statistical properties of the new distribution which includes: hazard function, moments, moment generating function, skewness, kurtosis, Renyl entropy and the order statistics were studied. A maximum likelihood estimation method was used in estimating the parameters of the distribution. Applications to real data set show the tractability of the distribution over other distributions and its sub-model.

scholarly journals An Extension of Log-Logistic Distribution for Analyzing Survival Data

2020 ◽  
pp. 789-801
Author(s):  
Aliya Syed Malik ◽  
S.P. Ahmad
Keyword(s):  
Survival Data ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Logistic Distribution ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
New Distribution

In this paper, a new generalization of Log Logistic Distribution using Alpha Power Transformation is proposed. The new distribution is named Alpha Power Log-Logistic Distribution. A comprehensive account of some of its statistical properties are derived. The maximum likelihood estimation procedure is used to estimate the parameters. The importance and utility of the proposed model are proved empirically using two real life data sets.

scholarly journals A Study of Convolution Models for Background Correction of BeadArrays

2016 ◽  
Vol 45 (2) ◽  
pp. 15-33
Author(s):  
Rohmatul Fajriyah
Keyword(s):  
Probability Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Parameters Estimation ◽  
Background Correction ◽  
Data Sets ◽  
Normal Model ◽  
Data Set ◽  
Convolution Model ◽  
Maximum Likelihood Estimation Method

The robust multi-array average (RMA), since its introduction in Irizarry, Bolstad,Collin, Cope, Hobbs, and Speed (2003a); Irizarry, Hobbs, Collin, Beazer-Barclay, An-tonellis, Scherf, and Speed (2003b); Irizarry, Wu, and Jaee (2006), has gained popularityamong bioinformaticians. It has evolved from the exponential-normal convolution to thegamma-normal convolution, from single to two channels and from the Aymetrix to theIllumina platform.The Illumina design provides two probe types: the regular and the control probes.This design is very suitable for studying the probability distribution of both and one canapply a convolution model to compute the true intensity estimator.In this paper, we study the existing convolution models for background correction ofIllumina BeadArrays in the literature and give a new estimator for the true intensity,assuming that the intensity value is exponentially or gamma distributed and the noise haslognormal distribution.Our study shows that one of our proposed models, the gamma-lognormal with themethod of moments for parameters estimation, is the optimal one for the benchmark-ing data set with benchmarking criteria, while the gamma-normal model has the bestperformance for the benchmarking data set with simulation criteria.For the publicly available data sets, the gamma-normal and the exponential-gammamodels with maximum likelihood estimation method can not be used and our proposedmodels exponential-lognormal and gamma-lognormal have the best performance, showinga moderate error in background correction and in the parametrization.

scholarly journals Chen Pareto Distribution:Properties and Application

2020 ◽  
pp. 812-826
Author(s):  
Phillip Awodutire
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Generating Functions ◽  
Pareto Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Extensive Simulation ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution ◽  
Family Of Distributions

In this work, a new distribution called the Chen Pareto distribution was derived using the Chen-G family of distributions. The mixture representation of the distribution was obtained. Furthermore, some statistical properties such as moments, moment generating functions, order statistics properties of the distribution were explored. The parameter estimation for the distribution was done using the maximum likelihood estimation method and the performance of estimators was assessed by conducting an extensive simulation study. The distribution was applied to a real dataset in which it performs best when compared to some related distributions

scholarly journals The Generalized Odd Gamma-G Family of Distributions: Properties and Applications

2018 ◽  
Vol 47 (2) ◽  
pp. 69-89 ◽  
Author(s):  
Bistoon Hosseini ◽  
Mahmoud Afshari ◽  
Morad Alizadeh
Keyword(s):  
Maximum Likelihood ◽  
Test Validity ◽  
Estimation Method ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Data Sets ◽  
Maximum Likelihood Estimation Method ◽  
Family Of Distributions

Recently, new continuous distributions have been proposed to apply in statistical analysis. In this paper, the Generalized Odd Gamma-G distribution is introduced. In particular, G has been considered as the Uniform distribution and some statistical properties such as quantile function, asymptotics, moments, entropy and order statistics have been calculated.The fitness capability of this model has been investigated  by fitting this model and others based on real data sets. The  parameters of this model are estimated by the maximum likelihood estimation method with simulated  real data in order to test validity of maximum likelihood estimators .

scholarly journals A New Generalized Weibull- Odd Frѐchet Family of Distributions: Statistical Properties and Applications

2020 ◽  
pp. 25-43
Author(s):  
A. Usman ◽  
S. I. S. Doguwa ◽  
B. B. Alhaji ◽  
A. T. Imam
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Order Statistics ◽  
Mean Squared Error ◽  
Moment Generating Function ◽  
Data Sets ◽  
Mathematical Properties ◽  
Squared Error ◽  
New Distribution ◽  
Family Of Distributions

We introduced a new generalized Weibull- Odd Frѐchet family of distributions with three extra parameters and we derived some of its structural properties. We derived comprehensive mathematical properties which include moments, moment generating function, Entropies and Order Statistics. One family of this distribution called new generalized Weibull- Odd Frѐchet -Frѐchet distribution is used to fit two data sets using the MLE procedure. A Monte Carlo simulation is used to test the robustness of the parameters of this distribution, in terms of the bias and mean squared error. The results of fitting this new distribution to two different data sets suggest that the new distribution outperforms its competitors.

scholarly journals The Beta Type I Generalized Half Logistic Distribution: Properties and Application

2020 ◽  
pp. 27-41
Author(s):  
P. O. Awodutire ◽  
E. C. Nduka ◽  
M. A. Ijomah
Keyword(s):  
Survival Function ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Logistic Distribution ◽  
Bladder Cancer Patient ◽  
Type I ◽  
Estimation Of Parameters ◽  
Survival Times ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

In a view to obtain a new distribution that is more exible than the type I generalized half logistic distribution, we used the beta-G generator and the type I generalized half logistic distribution. Some properties of the new distribution including the cummulative distribution function,survival function, hazard function were studied. Estimation of parameters were done using the maximum likelihood estimation method. Application of the derived distribution to lifetime data was illustrated by applying to remission times of bladder cancer patient data and survival times of guinea pigs.

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