scholarly journals The Equilibrium Renewal Burr XII Distribution: Properties and Applications

2021 ◽  
pp. 18-40
Author(s):  
Abdulzeid Yen Anafo ◽  
Lewis Brew ◽  
Suleman Nasiru
Keyword(s):  
Probability Distribution ◽  
Hazard Rate ◽  
Lorenz Curve ◽  
Hazard Function ◽  
Survival Function ◽  
Moment Generating Function ◽  
Mean Deviation ◽  
Reversed Hazard Rate ◽  
Burr Xii Distribution ◽  
Method Of Maximum Likelihood

In this paper, we propose a three-parameter probability distribution called equilibrium renewal Burr XII distribution using the equilibrium renewal process. The statistical properties of the distribution such as moment, mean deviation, order statistics, moment generating function, Beforroni and Lorenz curve, survival function, reversed hazard rate and hazard function were derived. The method of maximum likelihood is used for estimating the distribution's parameters and a simulation study is conducted to assess the performance of the parameters. We provide two applications in eld of health to demonstrate the importance of the proposed distribution.

scholarly journals A Weibull-Gompertz Makeham Distribution with Properties and Application to Cancer Data

2019 ◽  
pp. 1-17
Author(s):  
Peter O. Koleoso ◽  
Angela U. Chukwu
Keyword(s):  
Bladder Cancer ◽  
Maximum Likelihood ◽  
Order Statistics ◽  
Hazard Function ◽  
Probability Distributions ◽  
Survival Function ◽  
Statistical Properties ◽  
Cancer Data ◽  
Method Of Maximum Likelihood ◽  
Flexible Model

The article presents an extension of the Gompertz Makeham distribution using the Weibull-G family of continuous probability distributions proposed by Tahir et al. (2016a). This new extension generates a more flexible model called Weibull-Gompertz Makeham distribution. Some statistical properties of the distribution which include the moments, survival function, hazard function and distribution of order statistics were derived and discussed. The parameters were estimated by the method of maximum likelihood and the distribution was applied to a bladder cancer data. Weibull-Gompertz Makeham distribution performed best (AIC = -6.8677, CAIC = -6.3759, BIC = 7.3924) when compared with other existing distributions of the same family to model bladder cancer data.

scholarly journals The Iwok-Nwikpe Distribution: Statistical Properties and Its Application

2021 ◽  
pp. 35-45
Author(s):  
Iwok Iberedem Aniefiok ◽  
Barinaadaa John Nwikpe
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Survival Function ◽  
Medical Science ◽  
Mathematical Expression ◽  
Real Data ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Data Sets

In this paper, a new continuous probability distribution named Iwok-Nwikpe distribution is proposed. Some essential statistical properties of the proposed probability distribution have been derived. The graphs of the survival function, probability density function (p.d.f) and cumulative distribution function (c.d.f) were plotted at different values of the parameter. The mathematical expression for the moment generating function (mgf) was derived. Consequently, the first three crude moments were obtained; the distribution of order statistics, the second and third moments corrected for the mean have also been derived. The parameter of the Iwok-Nwikpe distribution was estimated by means of maximum likelihood technique. To establish the goodness of fit of the Iwok-Nwikpe distribution, three real data sets from engineering and medical science were fitted to the distribution. Findings of the study revealed that the Iwok-Nwikpe distribution performed better than the one parameter exponential distribution and other competing models used for the study.

scholarly journals On Properties and Applications of Lomax-Gompertz Distribution

2019 ◽  
pp. 1-17
Author(s):  
A. Omale ◽  
O. E. Asiribo ◽  
A. Yahaya
Keyword(s):  
Survival Function ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Gompertz Distribution ◽  
Probability Of Survival ◽  
Method Of Maximum Likelihood ◽  
Age Dependent ◽  
New Distribution

This article introduces a new distribution called the Lomax-Gompertz distribution developed through a Lomax Generator proposed in an earlier study. Some statistical properties of the proposed distribution comprising moments, moment generating function, characteristics function, quantile function and the distribution of order statistics were derived. The plots of the probability density function revealed that it is positively skewed. The model parameters have been estimated using the method of maximum likelihood. The plot the of survival function indicates that the Lomax-Gompertz distribution could be used to model time or age-dependent data, where probability of survival is believed to be  decreasing  with time or age. The performance of the Lomax-Gompertz distribution has been compared to other generalizations of the Gompertz distribution using three real-life datasets used in earlier researches.

scholarly journals THE BETA TRANSMUTED POWER DISTRIBUTION: PROPERTIES AND APPLICATION

2019 ◽  
Vol 3 (1) ◽  
pp. 105-123
Author(s):  
Abdelhakim Alabid ◽  
Ahmed Ali Hurairah ◽  
Indonesian Journal of Statistics and Its Applications IJSA
Keyword(s):  
Probability Distribution ◽  
Power Distribution ◽  
Asymptotic Variance ◽  
Real Data ◽  
Mean Deviation ◽  
Model Parameters ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
Asymptotic Confidence Intervals ◽  
New Distribution

In this this paper, we define and study a new generalization of the Power distribution and the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distribution taking Power distribution as the base distribution. The new distribution is called the beta transmuted Power (BTP) distribution. Some properties of the distribution such as moments, quantiles, mean deviation and order statistics are derived. The method of maximum likelihood is proposed to estimate the model parameters. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. A simulation study is conducted to study the performance of the estimators. The importance and flexibility of the new model is proved empirically using a real data set.

scholarly journals PCM Transformation: Properties and Their Estimation

2021 ◽  
Author(s):  
Dinesh Kumar ◽  
Pawan Kumar ◽  
Pradip Kumar ◽  
Sanjay Kumar Singh ◽  
Umesh Singh
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Stochastic Ordering ◽  
Information Criterion ◽  
Moment Generating Function ◽  
Rate Function ◽  
Hazard Rate Function ◽  
Test Statistic ◽  
Bayesian Approaches

In the present piece of work, we are going to propose a new trigonometry based transformation called PCM transformation. We have been obtained its various statistical properties such as survival function, hazard rate function, reverse-hazard rate function, moment generating function, median, stochastic ordering etc. Maximum Likelihood Estimator (MLE) method under classical approach and Bayesian approaches are tackled to obtain the estimate of unknown parameter. A real dataset has been applied to check its fitness on the basis of fitting criterions Akaike Information criterion (AIC), Bayesian Information criterion (BIC), log-likelihood (-LL) and Kolmogrov-Smirnov (KS) test statistic values in real sense. A simulation study is also being conducted to assess the estimator’s long-term attitude and compared over some chosen distributions.

scholarly journals Poisson Transmuted-G Family of Distributions: Its Properties and Applications

2021 ◽  
pp. 309-332 ◽  
Author(s):  
Laba Handique ◽  
Subrata Chakraborty ◽  
M.S. Eliwa ◽  
Dr. G.G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Failure Time ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Residual Lifetime ◽  
Mean Deviation ◽  
Time Data ◽  
Family Based ◽  
Family Of Distributions

In this article, an extension of the transmuted-G family is proposed, in the so-called Poison transmuted-G family of distributions. Some of its statistical properties including quantile function, moment generating function, order statistics, probability weighted moment, stress-strength reliability, residual lifetime, reversed residual lifetime, Rényi entropy and mean deviation are derived. A few important special models of the proposed family are listed. Stochastic characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function, are also studied. The family parameters are estimated via the maximum likelihood approach. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators. The advantage of the proposed family in data fitting is illustrated by means of two applications to failure time data sets.

scholarly journals A Transmuted Lomax-Exponential Distribution: Properties and Applications

2019 ◽  
pp. 1-13
Author(s):  
S. Kuje ◽  
K. E. Lasisi
Keyword(s):  
Exponential Distribution ◽  
Probability Distributions ◽  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Cumulative Distribution ◽  
Method Of Maximum Likelihood ◽  
New Distribution

In this article, the Quadratic rank transmutation map proposed and studied by Shaw and Buckley [1] is used to construct and study a new distribution called the transmuted Lomax-Exponential distribution (TLED) as an extension of the Lomax-Exponential distribution recently proposed by Ieren and Kuhe [2]. Using the transmutation map, we defined the probability density function and cumulative distribution function of the transmuted Lomax-Exponential distribution. Some properties of the new distribution such as moments, moment generating function, characteristics function, quantile function, survival function, hazard function and order statistics are also studied. The estimation of the distributions’ parameters has been done using the method of maximum likelihood estimation. The performance of the proposed probability distribution is being tested in comparison with some other generalizations of Exponential distribution using a real life dataset. The results obtained show that the TLED performs better than the other probability distributions.

scholarly journals On a new distribution based on the arccosine function

2021 ◽  
Author(s):  
Christophe Chesneau ◽  
Lishamol Tomy ◽  
Jiju Gillariose
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Power Functions ◽  
New Distribution

AbstractThis note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be “round mesokurtic” and “left skewed”. With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

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