scholarly journals On a Power Transformation of Half-Logistic Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
S. D. Krishnarani
Keyword(s):  
Real Line ◽  
Continuous Distribution ◽  
Real Life ◽  
Logistic Distribution ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Positive Real ◽  
Real Life Data ◽  
New Distribution ◽  
Positive Real Line

A new continuous distribution on the positive real line is constructed from half-logistic distribution, using a transformation and its analytical characteristics are studied. Some characterization results are derived. Classical procedures for the estimation of parameters of the new distribution are discussed and a comparative study is done through numerical examples. Further, different families of continuous distributions on the positive real line are generated using this distribution. Application is discussed with the help of real-life data sets.

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 Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

scholarly journals An extensive extension of exponentiated exponential distribution using alpha power transformation – statistical properties and applications in engineering science

2021 ◽  
Vol 17 (2) ◽  
pp. 59-74
Author(s):  
S. Qurat Ul Ain ◽  
K. Ul Islam Rather
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Statistical Properties ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean Variance ◽  
New Distribution ◽  
Extra Parameter

Abstract In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

scholarly journals The Gompertz Gumbel II Distribution: Properties and Applications

2020 ◽  
pp. 1-15
Author(s):  
Adebisi Ade Ogunde ◽  
Gbenga Adelekan Olalude ◽  
Donatus Osaretin Omosigho
Keyword(s):  
Real Life ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Life Data ◽  
Real Life Data ◽  
Decreasing Failure Rate ◽  
New Distribution

In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.

scholarly journals On the inferences and applications of transmuted exponential Lomax distribution

2018 ◽  
Vol 6 (1) ◽  
pp. 30
Author(s):  
Umar Kabir ◽  
Terna Godfrey IEREN
Keyword(s):  
Real Life ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Probability Density Function Pdf ◽  
New Distribution ◽  
Better Than

This article proposed a new distribution referred to as the transmuted Exponential Lomax distribution as an extension of the popular Lomax distribution in the form of Exponential Lomax by using the Quadratic rank transmutation map proposed and studied in earlier research. Using the transmutation map, we defined the probability density function (PDF) and cumulative distribution function (CDF) of the transmuted Exponential Lomax distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Lomax distribution using three real-life data sets. The results obtained indicated that TELD performs better than the other distributions comprising power Lomax, Exponential-Lomax, and the Lomax distributions.

scholarly journals A Poisson XLindley Distribution with Applications

2021 ◽  
Author(s):  
Fatma Zohra Seghier ◽  
Halim Zeghdoudi
Keyword(s):  
Method Of Moments ◽  
Nipah Virus ◽  
Continuous Distribution ◽  
Real Life ◽  
Factorial Moment ◽  
Real Data ◽  
Data Sets ◽  
Data Set ◽  
Real Life Data ◽  
Method Of Maximum Likelihood

Abstract In this paper, a Poisson XLindley distribution (PXLD) has been obtained by compounding Poisson (PD) distribution with a continuous distribution. A general expression for its rth factorial moment about origin has been derived and hence its raw moments and central moments are obtained. The expressions for its coefficient of variation, skewness, kurtosis and index of dispersion have also been given. In particular, the method of maximum likelihood and the method of moments for the estimation of its parameters have been discussed. Finally, two real-life data sets are analyzed to investigate the suitability of the proposed distribution in modeling a real data set on Nipah virus infection, number of Hemocytometer yeast cell count data and epileptic seizure counts data.

scholarly journals Some Properties and Applications of Topp Leone Kumaraswamy Lomax Distribution

2021 ◽  
Vol 3 (2) ◽  
pp. 81-94
Author(s):  
Sule Ibrahim ◽  
Sani Ibrahim Doguwa ◽  
Audu Isah ◽  
Haruna, M. Jibril
Keyword(s):  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Data Sets ◽  
Lifetime Distributions ◽  
Air Conditioning System ◽  
Lomax Distribution ◽  
Real Life Data ◽  
New Distribution

Many Statisticians have developed and proposed new distributions by extending the existing distributions. The distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime distribution called the Topp Leone Kumaraswamy Lomax distribution was introduced by using a family of distributions which has been proposed in the literature. Some mathematical properties of the distribution such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions were presented. The estimation of the parameters by maximum likelihood method was discussed. Three real life data sets representing the failure times of the air conditioning system of an air plane, the remission times (in months) of a random sample of one hundred and twenty-eight (128) bladder cancer patients and Alumina (Al2O3) data were used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in the three datasets considered.

scholarly journals The Transmuted Muth Generated Class of Distributions with Applications

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1677
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Survival Data ◽  
Natural Extension ◽  
Real Life ◽  
Environmental Data ◽  
Logistic Distribution ◽  
Data Sets ◽  
New Class ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean And Variance

Recently, the Muth generated class of distributions has been shown to be useful for diverse statistical purposes. Here, we make some contributions to this class by first discussing new theoretical facts and then introducing a natural extension of it via the transmuted scheme. The extended class is described in detail, emphasizing the characteristics of its probability and reliability functions, as well as its moments. Among other things, we show that it can extend the possible values of the mean and variance of the parental distribution, while maintaining symmetry or creating various types of asymmetry. The mathematical inference of the parameters is also discussed. Special attention is paid to the distribution of the new class using the log-logistic distribution as a parent. In an applied work, we evaluate the behavior of the corresponding model by using simulated and practical data. In particular, we employ it to fit two real-life data sets, one with environmental data and the other with survival data. Standard statistical criteria validate the importance of the proposed model.

scholarly journals A New Extended Burr XII Distribution

2017 ◽  
Vol 46 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Indranil Ghosh ◽  
Marcelo Bourguinon
Keyword(s):  
Real Life ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Burr Xii Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Proposed Model ◽  
New Distribution

In this paper, we propose a new lifetime distribution, namely the extended Burr XII distribution (using the technique as mentioned in Cordeiro et al. (2015)). We derive some basic properties of the new distribution and provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates of model parameters. For illustrative purposes, two real life data sets have been considered as an application of the proposed model.

scholarly journals Tornumonkpe Distribution: Statistical Properties and Goodness of Fit

2021 ◽  
pp. 12-22
Author(s):  
Barinaadaa John Nwikpe
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Mathematical Expression ◽  
Information Criterion ◽  
Moment Generating Function ◽  
Data Sets ◽  
The Moment ◽  
The One ◽  
Coefficient Of Skewness ◽  
New Distribution

A new sole parameter probability distribution named the Tornumonkpe distribution has been derived in this paper. The new model is a blend of gamma (2,  and gamma(3  distributions. The shape of its density for different values of the parameter has been shown.  The mathematical expression for the moment generating function, the first three raw moments, the second and third moments about the mean, the distribution of order statistics, coefficient of variation and coefficient of skewness has been given. The parameter of the new distribution was estimated using the method of maximum likelihood. The goodness of fit of the Tornumonkpe distribution was established by fitting the distribution to three real life data sets. Using -2lnL, Bayesian Information Criterion (BIC), and Akaike Information Criterion(AIC) as criterial for selecting the best fitting model, it was revealed that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used.

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