scholarly journals A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 711
Author(s):  
Rana Ali Bakoban ◽  
Ashwaq Mohammad Al-Shehri
Keyword(s):  
Generalized Inverse ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Information Criteria ◽  
Difference Fields ◽  
The Mean

In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliability function, and hazard function are studied. Next, we derived the quantile function, median, mode, moments, harmonic mean, skewness, and kurtosis. In addition, the order statistics and the mean deviations about the mean and median are found. Other important properties including entropy (Rényi and Shannon), which is a measure of the uncertainty for this distribution, are also investigated. Maximum likelihood estimation is adopted to the model. A simulation study is conducted to estimate the parameters. Four real-life data sets from difference fields were applied on this model. In addition, a comparison between the new model and some competitive models is done via information criteria. Our model shows the best fitting for the real data.

scholarly journals The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data

2021 ◽  
Vol 3 (2) ◽  
pp. 65-80
Author(s):  
Usman Aliyu Abdullahi ◽  
Ahmad Abubakar Suleiman ◽  
Aliyu Ismail Ishaq ◽  
Abubakar Usman ◽  
Aminu Suleiman
Keyword(s):  
Exponential Distribution ◽  
Survival Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Information Criteria ◽  
Cumulative Distribution ◽  
Two Parameters ◽  
Maximum Likelihood Estimation Method

Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell – Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.

scholarly journals A generalization to the log-inverse Weibull distribution and its applications in cancer research

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
C. Satheesh Kumar ◽  
Subha R. Nair
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Life ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Reliability Function ◽  
Rate Function ◽  
Data Sets ◽  
Inverse Weibull Distribution

AbstractIn this paper we consider a generalization of a log-transformed version of the inverse Weibull distribution. Several theoretical properties of the distribution are studied in detail including expressions for its probability density function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, percentile measures, entropy measures, median, mode etc. Certain structural properties of the distribution along with expressions for reliability measures as well as the distribution and moments of order statistics are obtained. Also we discuss the maximum likelihood estimation of the parameters of the proposed distribution and illustrate the usefulness of the model through real life examples. In addition, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated data sets.

scholarly journals A New Odd Lindley-Gompertz Distribution: Its Properties and Applications

2020 ◽  
pp. 29-47
Author(s):  
Omolola Dorcas Atanda ◽  
Tajan Mashingil Mabur ◽  
Gerald Ikechukwu Onwuka
Keyword(s):  
Generating Function ◽  
Hazard Function ◽  
Goodness Of Fit ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Reliability Function ◽  
Moment Generating Function ◽  
Gompertz Distribution ◽  
Better Than

This article presents a comprehensive study of an odd Lindley-Gompertz distribution which has already been proposed in the literature but without any properties. The present study unlike the previous one has considered the derivation of several properties of the odd Lindley-Gompertz distribution with their graphical representations and discussions which has not been done in the first proposition of the distribution.  The study looks at properties such as survival (or reliability) function, the hazard function, the cumulative hazard function, the reverse hazard function, the odds function, quantile function, moments, moment generating function, characteristic function, cumulant generating function, distribution of order statistics and maximum likelihood estimation of the distribution’s parameters none of which was treated by the previous author of the model. An illustration to evaluate the goodness-of-fit of the odd Lindley-Gompertz distribution has also been done using two real life datasets and the results show that the model fits the datasets better than the five other distributions considered in this present study.

scholarly journals Exponentiated Cubic Transmuted Weibull Distribution: Properties and Application

2021 ◽  
pp. 1-11
Author(s):  
Oseghale O. I. ◽  
Akomolafe A. A. ◽  
Gayawan E.
Keyword(s):  
Weibull Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Estimation Technique ◽  
Life Data ◽  
Real Life Data

This work is focused on the four parameters Exponentiated Cubic Transmuted Weibull distribution which mostly found its application in reliability analysis most especially for data that are non-monotone and Bi-modal. Structural properties such as moment, moment generating function, Quantile function, Renyi entropy, and order statistics were investigated. The maximum likelihood estimation technique was used to estimate the parameters of the distribution. Application to two real-life data sets shows the applicability of the distribution in modeling real data.

Cubic Transmuted-G Family of Distributions and Its Properties

2018 ◽  
Vol 33 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Information Criteria ◽  
Data Sets ◽  
New Family ◽  
Family Of Distributions

Abstract In this article, a new family of distributions is introduced by using transmutation maps. The proposed family of distributions is expected to be useful in modeling real data sets. The genesis of the proposed family, including several statistical and reliability properties, is presented. Methods of estimation like maximum likelihood, least squares, weighted least squares, and maximum product spacing are discussed. Maximum likelihood estimation under censoring schemes is also considered. Further, we explore some special models of the proposed family of distributions and examined different properties of these special models. We compare three particular models of the proposed family with several existing distributions using different information criteria. It is observed that the proposed particular models perform better than different competing models. Applications of the particular models of the proposed family of distributions are finally presented to establish the applicability in real life situations.

Mathematical properties of the Kumaraswamy-Lindley distribution and its applications

2017 ◽  
Vol 5 (1) ◽  
pp. 17
Author(s):  
Hamdy Salem ◽  
Abd-Elwahab Hagag
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Least Square ◽  
Estimation Of Parameters ◽  
Least Square Estimation ◽  
Mathematical Properties ◽  
Composite Distribution

In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

scholarly journals The New Novel Discrete Distribution with Application on COVID-19 Mortality Numbers in Kingdom of Saudi Arabia and Latvia

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
M. Nagy ◽  
Ehab M. Almetwally ◽  
Ahmed M. Gemeay ◽  
Heba S. Mohammed ◽  
Taghreed M. Jawa ◽  
...  
Keyword(s):  
Saudi Arabia ◽  
Statistical Model ◽  
Discrete Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Linear Representation ◽  
Quantile Function ◽  
Mortality Data ◽  
Unknown Parameters ◽  
New Novel

This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and modeling this kind of discrete data. Also, we provide a graphical plot for the data to ensure our results.

scholarly journals A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1394
Author(s):  
Mustapha Muhammad ◽  
Huda M. Alshanbari ◽  
Ayed R. A. Alanzi ◽  
Lixia Liu ◽  
Waqas Sami ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Weibull Model ◽  
Mean Square ◽  
Reliability Parameter ◽  
Coverage Probabilities ◽  
The Mean

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

scholarly journals On the Extended Generalized Inverse Exponential Distribution with Its Applications

2020 ◽  
pp. 14-27
Author(s):  
Sule Ibrahim ◽  
Bello Olalekan Akanji ◽  
Lawal Hammed Olanrewaju
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Generalized Inverse ◽  
Real Data ◽  
Quantile Function ◽  
Exponential Model ◽  
Data Sets ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Inverse Exponential Distribution

We propose a new distribution called the extended generalized inverse exponential distribution with four positive parameters, which extends the generalized inverse exponential distribution. We derive some mathematical properties of the proposed model including explicit expressions for the quantile function, moments, generating function, survival, hazard rate, reversed hazard rate and odd functions. The method of maximum likelihood is used to estimate the parameters of the distribution. We illustrate its potentiality with applications to two real data sets which show that the extended generalized inverse exponential model provides a better fit than other models considered.

scholarly journals Transmutation of the two parameters Rayleigh distribution

2016 ◽  
Vol 4 (2) ◽  
pp. 95
Author(s):  
Ehsan Ullah ◽  
Mirza Shahzad
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Least Square Estimation ◽  
Proposed Model ◽  
Method Of Least Square ◽  
Two Parameters ◽  
Mean Variance

In this study, transmuted two parameters Rayleigh distribution is proposed using quadratic rank transmutation map. This proposed distribution is more flexible and versatile than two parameters Rayleigh distribution. Some properties of the proposed distribution are derived such as moments, moment generating function, mean, variance, median, quantile function, reliability, and hazard function. The parameter estimation is approached through the method of least square estimation. The th and joint order statistics are also derived for the proposed distribution. The application of proposed model illustrated and compared using real data.

Sign in / Sign up

Export Citation Format

Share Document