scholarly journals Transmuted Modified Weibull distribution: Properties and Application

2018 ◽  
Vol 11 (2) ◽  
pp. 362-374
Author(s):  
Muhammad Shuaib Khan ◽  
Robert King ◽  
Irene L. Hudson
Keyword(s):  
Weibull Distribution ◽  
Survival Data ◽  
Model Parameters ◽  
Hazard Functions ◽  
Method Of Maximum Likelihood ◽  
The Mean ◽  
Moment Approach ◽  
Modified Weibull ◽  
Coefficient Of Skewness ◽  
Mean Variance

This research investigates the potential usefulness of the transmutedmodified Weibull distribution for modelling lifetime data. Weattain the diagnostic shapes of the density and hazard functions. Weformulate the expressions for the moments,incomplete moments, Renyientropy and q- entropy. We estimate the mean, variance, coefficientof variation, coefficient of skewness and coefficient of kurtosis basedon moment approach. The method of maximum likelihood is used forestimating the model parameters. We illustrate the use of transmutedmodified Weibull distribution with an application to survival data.

scholarly journals The Beta Transmuted Weibull Distribution

2014 ◽  
Vol 43 (2) ◽  
pp. 133-149 ◽  
Author(s):  
Manisha Pal ◽  
Montip Tiensuwan
Keyword(s):  
Weibull Distribution ◽  
Censored Data ◽  
Weibull Model ◽  
Model Parameters ◽  
Lorenz Curves ◽  
Positive Data ◽  
Method Of Maximum Likelihood ◽  
Special Cases ◽  
The Mean ◽  
New Distribution

The paper introduces a beta transmuted Weibull distribution, which contains a number ofdistributions as special cases. The properties of the distribution are discussed and explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, and reliability. The distribution and moments of order statistics are also studied. Estimation of the model parameters by the method of maximum likelihood is discussed. The log beta transmuted Weibull model is introduced to analyze censored data. Finally, the usefulness of the new distribution in analyzing positive data is illustrated.

scholarly journals A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qinghu Liao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Functions ◽  
Practical Applications ◽  
Nonnested Models

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

scholarly journals Comparative Study of Reliability of Some Antiseptic Soaps; A 3- Parameter Weibull Distribution

2015 ◽  
Vol 1 (01) ◽  
Author(s):  
Olubiyi O. A.
Keyword(s):  
Maximum Likelihood ◽  
Comparative Study ◽  
Weibull Distribution ◽  
Dissolution Time ◽  
Time To Failure ◽  
Likelihood Estimator ◽  
Method Of Maximum Likelihood ◽  
Mean And Variance ◽  
The Mean ◽  
Parameter Case

This study was carried out to estimate the dissolution time of some antiseptic soaps . The lifetime behavior of the antiseptic soaps was also modeled in order to estimate some basic measures and compare their lifetimes. In the analysis of data, the weibull distribution of 3-parameter case was used. The method of maximum likelihood estimator was used in estimating the parameters. The mean and variance time to failure, reliability, Weibull conditional reliability and Weibull reliable life of the products were obtained.

scholarly journals A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2768
Author(s):  
Luis Sánchez ◽  
Víctor Leiva ◽  
Helton Saulo ◽  
Carolina Marchant ◽  
José M. Sarabia
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Quantile Regression ◽  
Regression Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Distributed Data ◽  
Quantile Regression Model ◽  
The Mean ◽  
Asymmetrically Distributed

Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.

The Marshall-olkin Inverse Lomax Distribution (MO-ILD) with Application on Cancer Stem Cell

2019 ◽  
pp. 1-12 ◽  
Author(s):  
Obubu Maxwell ◽  
Angela Unna Chukwu ◽  
Oluwafemi Samuel Oyamakin ◽  
Mundher A. Khaleel
Keyword(s):  
Stem Cell ◽  
Cancer Stem Cell ◽  
Weibull Distribution ◽  
Model Parameters ◽  
Data Types ◽  
Lomax Distribution ◽  
Method Of Maximum Likelihood ◽  
Compound Distribution ◽  
Inverse Lomax Distribution ◽  
Cell Data

A new compound distribution called the Marshall-Olkin Inverse Lomax distribution (MO-ILD) was proposed, extending the inverse Lomax distribution by adding a new parameter to the existing distribution, leading to greater flexibility in modeling various data types. Its basic statistical properties were derived and model parameters estimated using the method of maximum likelihood. The Proposed distribution was applied to Cancer Stem Cell data and compared to the Marshall Olkin Flexible Weibull Extension Distribution (MO-FWED), and the Marshall-Olkin exponential Weibull distribution (MO-EWD). The Marshall-Olkin Inverse Lomax distribution provided a better fit than the Marshall Olkin Flexible Weibull Extension Distribution, and the Marshall-Olkin exponential Weibull distribution based on log-likelihood AIC, CAIC, BIC and HQIC values.

Spatial modelling of total storm rainfall

1986 ◽  
Vol 403 (1824) ◽  
pp. 27-50 ◽  
Keyword(s):  
Covariance Structure ◽  
Random Variable ◽  
Spatial Modelling ◽  
Storm Event ◽  
Model Parameters ◽  
Random Parameters ◽  
Spread Function ◽  
The Mean ◽  
Storm Rainfall ◽  
Mean Variance

The spatial structure of the depth of rainfall from a stationary storm event is investigated by using point process techniques. Cells are assumed to be stationary and to be distributed in space either independently according to a Poisson process, or with clustering according to a Neyman-Scott scheme. Total storm rainfall at the centre of each cell is a random variable and rainfall is distributed around the centre in a way specified by a spread function that may incorporate random parameters. The mean, variance and covariance structure of the precipitation depth at a point are obtained for different spread functions. For exponentially distributed centre depth and a spread function having quadratically exponential decay, the total storm depth at any point in the field is shown to have a gamma distribution. The probability of zero rainfall at a point is investigated, as is the stochastic variability of model parameters from storm to storm. Data from the Upper Rio Guaire basin in Venezuela are used in illustration.

scholarly journals A New Lifetime Exponential-X Family of Distributions with Applications to Reliability Data

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Xiaoyan Huo ◽  
Saima K. Khosa ◽  
Zubair Ahmad ◽  
Zahra Almaspoor ◽  
Muhammad Ilyas ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Model Parameters ◽  
Reliability Engineering ◽  
Reliability Data ◽  
Monte Carlo Simulation Study ◽  
Hazard Functions ◽  
Practical Applications ◽  
New Family ◽  
Nonnested Models ◽  
Family Of Distributions

Modeling reliability data with nonmonotone hazards is a prominent research topic that is quite rich and still growing rapidly. Many studies have suggested introducing new families of distributions to modify the Weibull distribution to model the nonmonotone hazards. In the present study, we propose a new family of distributions called a new lifetime exponential-X family. A special submodel of the proposed family called a new lifetime exponential-Weibull distribution suitable for modeling reliability data with bathtub-shaped hazard rates is discussed. The maximum-likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is conducted to evaluate the performance of these estimators. For illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

Bayesian mixture cure rate frailty models with an application to gastric cancer data

2020 ◽  
pp. 096228022097469
Author(s):  
Ali Karamoozian ◽  
Mohammad Reza Baneshi ◽  
Abbas Bahrampour
Keyword(s):  
Gastric Cancer ◽  
Bayesian Inference ◽  
Weibull Distribution ◽  
Survival Data ◽  
Random Variable ◽  
Frailty Models ◽  
Accurate Estimation ◽  
Cure Rate ◽  
Generalized Modified Weibull ◽  
Modified Weibull

Mixture cure rate models are commonly used to analyze lifetime data with long-term survivors. On the other hand, frailty models also lead to accurate estimation of coefficients by controlling the heterogeneity in survival data. Gamma frailty models are the most common models of frailty. Usually, the gamma distribution is used in the frailty random variable models. However, for survival data which are suitable for populations with a cure rate, it may be better to use a discrete distribution for the frailty random variable than a continuous distribution. Therefore, we proposed two models in this study. In the first model, continuous gamma as the distribution is used, and in the second model, discrete hyper-Poisson distribution is applied for the frailty random variable. Also, Bayesian inference with Weibull distribution and generalized modified Weibull distribution as the baseline distribution were used in the two proposed models, respectively. In this study, we used data of patients with gastric cancer to show the application of these models in real data analysis. The parameters and regression coefficients were estimated using the Metropolis with Gibbs sampling algorithm, so that this algorithm is one of the crucial techniques in Markov chain Monte Carlo simulation. A simulation study was also used to evaluate the performance of the Bayesian estimates to confirm the proposed models. Based on the results of the Bayesian inference, it was found that the model with generalized modified Weibull and hyper-Poisson distributions is a suitable model in practical study and also this model fits better than the model with Weibull and Gamma distributions.

scholarly journals A family of Gamma-generated distributions: Statistical properties and applications

2021 ◽  
pp. 096228022110092
Author(s):  
Hormatollah Pourreza ◽  
Ezzatallah Baloui Jamkhaneh ◽  
Einolah Deiri
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Hazard Functions ◽  
Distribution Probability ◽  
Method Of Maximum Likelihood ◽  
Special Case

In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets. Mathematics Subject Classification: 62E99; 62E15

scholarly journals A New Generalized Log-logistic and Modified Weibull Distribution with Applications

2018 ◽  
Vol 7 (3) ◽  
pp. 72
Author(s):  
Broderick O. Oluyede ◽  
Huybrechts F. Bindele ◽  
Boikanyo Makubate ◽  
Shujiao Huang
Keyword(s):  
Hazard Function ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Lorenz Curves ◽  
Conditional Moments ◽  
Method Of Maximum Likelihood ◽  
Special Cases ◽  
L Moments ◽  
Modified Weibull

A new generalized distribution called the {\em log-logistic modified Weibull} (LLoGMW) distribution is presented. This distribution includes many submodels such as the log-logistic modified Rayleigh, log-logistic modified exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh and exponential distributions as special cases. Structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and R\'enyi entropy are derived. Model parameters are estimated based on the method of maximum likelihood. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.

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