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.

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 A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals The Half-Logistic Generalized Weibull Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Amna Bibi
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Type I ◽  
Failure Rate Function ◽  
New Model ◽  
Compound Distribution

A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher’s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

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 Generalized Modification of the Kumaraswamy Distribution for Modeling and Analyzing Real-Life Data

2020 ◽  
Vol 8 (2) ◽  
pp. 521-548
Author(s):  
Rafid Alshkaki
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Kumaraswamy Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Beta Power ◽  
Special Cases

In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefulness and the flexibility of this distribution in application to real-life data.  

scholarly journals A Novel Generator of Continuous Probability Distributions for the Asymmetric Left-skewed Bimodal Real-life Data with Properties and Copulas

2021 ◽  
pp. 943-961 ◽  
Author(s):  
Wahid A. M. Shehata ◽  
Haitham Yousof ◽  
Mohamed Aboraya
Keyword(s):  
Probability Distributions ◽  
Real Life ◽  
Real Data ◽  
Moment Generating Function ◽  
Data Sets ◽  
Base Line ◽  
Survival Times ◽  
New Family ◽  
Real Life Data ◽  
Two Parameter

This paper presents a novel two-parameter G family of distributions. Relevant statistical properties such as the ordinary moments, incomplete moments and moment generating function are derived.  Using common copulas, some new bivariate type G families are derived. Special attention is devoted to the standard exponential base line model. The density of the new exponential extension can be “asymmetric and right skewed shape” with no peak, “asymmetric right skewed shape” with one peak, “symmetric shape” and “asymmetric left skewed shape” with one peak. The hazard rate of the new exponential distribution can be “increasing”, “U-shape”, “decreasing” and “J-shape”. The usefulness and flexibility of the new family is illustrated by means of two applications to real data sets. The new family is compared with many common G families in modeling relief times and survival times data sets.

scholarly journals Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution

2020 ◽  
Vol 9 (6) ◽  
pp. 90
Author(s):  
A. A. Ogunde ◽  
S. T. Fayose ◽  
B. Ajayi ◽  
D. O. Omosigho
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Real Life ◽  
Simulation Method ◽  
Quantile Function ◽  
Transformation Method ◽  
Model Parameters ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data

In this work, we introduce a new generalization of the Inverted Weibull distribution called the alpha power Extended Inverted Weibull distribution using the alpha power transformation method. This approach adds an extra parameter to the baseline distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and moment generating functions, reliability analysis, Lorenz and Bonferroni and curves, Rényi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Simulation method and three real life data sets are presented to demonstrate the effectiveness of the new model.

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 Weighted Version of Generalized Inverse Weibull Distribution

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Sofi Mudasir ◽  
S. P. Ahmad
Keyword(s):  
Weibull Distribution ◽  
Generalized Inverse ◽  
Real Life ◽  
Moment Generating Function ◽  
Weighted Version ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Inverse Weibull Distribution ◽  
Better Than

Weighted distributions are used in many fields, such as medicine, ecology, and reliability. A weighted version of the generalized inverse Weibull distribution, known as weighted generalized inverse Weibull distribution (WGIWD), is proposed. Basic properties including mode, moments, moment generating function, skewness, kurtosis, and Shannon’s entropy are studied. The usefulness of the new model was demonstrated by applying it to a real-life data set. The WGIWD fits better than its submodels, such as length biased generalized inverse Weibull (LGIW), generalized inverse Weibull (GIW), inverse Weibull (IW) and inverse exponential (IE) distributions.

scholarly journals Generalized Rank Mapped Transmuted Distributions with Properties and Application: A Review

2021 ◽  
pp. 44-61
Author(s):  
. Imliyangba ◽  
Bhanita Das ◽  
Seema Chettri
Keyword(s):  
Probability Distributions ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Hazard Functions ◽  
Life Data ◽  
New Family ◽  
Real Life Data ◽  
Non Gaussian

Generalizing probability distributions is a very common practice in the theory of statistics. Researchers have proposed several generalized classes of distributions which are very flexible and convenient to study various statistical properties of the distribution and its ability to fit the real-life data. Several methods are available in the literature to generalize new family of distributions. The Quadratic Rank Transmutation Map (QRTM) is a tool for the construction of new families of non-Gaussian distributions and to modulate a given base distribution for modifying the moments like the skewness and kurtosis with the ability to explore its tail properties and improve the adequacy of the distribution. Recently, a new family of transmutation map, defined as Cubic Rank Transmutation (CRT) has been used by several authors to develop new distributions with application to real-life data. In this article, we have done a review work on the existing generalized rank mapped transmuted probability distributions, available in the literature with various statistical properties such as the reliability, hazard rate and cumulative hazard functions, moments, mean, variance, moment-generating function, order statistics, generalized entropy and quantile function along with its applications. Some future works have also been discussed for generalized rank mapped transmuted distributions.

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