scholarly journals A NEW FOUR-PARAMETER WEIBULL DISTRIBUTION WITH APPLICATION TO FAILURE TIME DATA

2020 ◽  
Vol 4 (3) ◽  
pp. 563-575
Author(s):  
Aminu Suleiman Mohammed ◽  
Fidelis Ifeanyi Ugwuowo
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Failure Time ◽  
Real Life ◽  
Model Parameters ◽  
Time Data ◽  
Lifetime Model ◽  
Estimation Of Model Parameters ◽  
Parameter Values ◽  
Maximum Likelihood Technique

A lifetime model called Transmuted Exponential-Weibull Distribution was proposed in this research. Several statistical properties were derived and presented in an explicit form. Maximum likelihood technique is employed for the estimation of model parameters, and a simulation study was performed to examine the behavior of various estimates under different sample sizes and initial parameter values. Through using real-life datasets, it was empirically shown that the new model provides sufficient fits relative to other existing models.

scholarly journals The Transmuted Marshall-Olkin Fr\'{e}chet Distribution: Properties and Applications

2015 ◽  
Vol 4 (4) ◽  
pp. 132 ◽  
Author(s):  
Ahmed Z. Afify ◽  
G. G. Hamedani ◽  
Indranil Ghosh ◽  
M. E. Mead
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Maximum Likelihood Method ◽  
Real Life ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Life Data ◽  
Real Life Data ◽  
Lifetime Model

<p>This paper introduces a new four-parameter lifetime model, which extends the Marshall-Olkin Fr\'{e}chet distribution introduced by Krishna et al. (2013), called the transmuted Marshall-Olkin Fr\'{e}chet distribution. Various structural properties including ordinary and incomplete moments, quantile and generating function, R\'{e}nyi and q-entropies and order statistics are<br />derived. The maximum likelihood method is used to estimate the model parameters. We illustrate the superiority of the proposed distribution over other existing distributions in the literature in modeling two real life data sets.</p>

scholarly journals Sine Inverse Lomax Generated Family of Distributions with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Aisha Fayomi ◽  
Ali Algarni ◽  
Abdullah M. Almarashi
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
New Family ◽  
Estimation Of Model Parameters ◽  
Generated Family ◽  
Family Of Distributions

This paper introduces a new family of distributions by combining the sine produced family and the inverse Lomax generated family. The new proposed family is very interested and flexible more than some old and current families. It has many new models which have many applications in physics, engineering, and medicine. Some fundamental statistical properties of the sine inverse Lomax generated family of distributions as moments, generating function, and quantile function are calculated. Four special models as sine inverse Lomax-exponential, sine inverse Lomax-Rayleigh, sine inverse Lomax-Frèchet and sine inverse Lomax-Lomax models are proposed. Maximum likelihood estimation of model parameters is proposed in this paper. For the purpose of evaluating the performance of maximum likelihood estimates, a simulation study is conducted. Two real life datasets are analyzed by the sine inverse Lomax-Lomax model, and we show that providing flexibility and more fitting than known nine models derived from other generated families.

scholarly journals KAJIAN RELIABILITAS PADA SISTEM SERI-PARALEL DENGAN EMPAT KOMPONEN

2018 ◽  
Vol 7 (1) ◽  
pp. 73-83
Author(s):  
Farhah Izzatul Jannah ◽  
Sudarno Sudarno ◽  
Alan Prahutama
Keyword(s):  
Weibull Distribution ◽  
System Reliability ◽  
Failure Time ◽  
Likelihood Estimation ◽  
Parallel System ◽  
Operating Conditions ◽  
Failure Time Data ◽  
Time Data ◽  
Rank Regression ◽  
Load Resistor

Reliability analysis is the analysis of the possibility that the product or service will function properly for a certain period of time under operating conditions without failure. One configuration of components that can be formed is a series-parallel system on a filter capacitor circuit using 4 components consisting of 2 rectifier diodes, 1 capacitor, and 1 load resistor. The data used to obtain the value of system reliability is the time of failure based on the assumption of failure of the independent component. The function of the form on the system can be expressed by Ф(x)= x1x3 + x1x4 + x2x3 + x2x4 - x1x3x4 - x2x3x4 - x1x2x3 - x1x2x4 + x1x2x3x4. The parameter values of each distribution are calculated using the Median Rank Regression Estimation (MRRE) and Maximum Likelihood Estimation (MLE) methods. To test the data following a certain distribution or not, the calculation is manually done with the Anderson-Darling (AD) test so that it is known that the failure time data of rectifier diode 1 follows the weibull distribution with parameters  and , failure time data of rectifier diode 2 follows weibull distribution with parameters  and , failure time data of capacitors follow normal distribution with parameters  and , and the failure time data of the load resistor following the gamma distribution with parameters  and . From the calculation of system reliability, it shows that the higher the intensity of the system fails it will affect the value of reliability to be lower. A serial system from a parallel system functions if there is at least one component j in one subsystem that functions. Keywords: Reliability, Series-Parallel, MRRE, MLE, AD.

scholarly journals Kumaraswamy Transmuted Exponentiated Additive Weibull Distribution

2016 ◽  
Vol 5 (2) ◽  
pp. 78 ◽  
Author(s):  
Zohdy M. Nofal ◽  
Ahmed Z. Afify ◽  
Haitham M. Yousof ◽  
Daniele C. T. Granzotto ◽  
Francisco Louzada
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Hazard Function ◽  
Quantile Function ◽  
Special Cases ◽  
Lifetime Model ◽  
Mean Variance ◽  
Probabilistic Measures

This paper introduces a new lifetime model which is a generalization of the transmuted exponentiated additive Weibull distribution by using the Kumaraswamy generalized (Kw-G) distribution. With the particular case no less than \textbf{seventy nine} sub models as special cases, the so-called Kumaraswamy transmuted exponentiated additive Weibull distribution, introduced by Cordeiro and de Castro (2011) is one of this particular cases. Further, expressions for several probabilistic measures are provided, such as probability density function, hazard function, moments, quantile function, mean, variance and median, moment generation function, R\'{e}nyi and q entropies, order estatistics, etc. Inference is maximum likelihood based and the usefulness of the model is showed by using a real dataset.

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

scholarly journals The Generalized Ampadu-G Family of Distributions: Properties, Applications and Characterizations

2020 ◽  
pp. 139-167
Author(s):  
Clement Boateng Ampadu ◽  
Abdulzeid Yen Anafo
Keyword(s):  
Weibull Distribution ◽  
Density Function ◽  
Survival Function ◽  
Real Life ◽  
Life Time ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Model Parameters ◽  
New Family ◽  
Family Of Distributions

This paper introduces a new class of distributions called the generalized Ampadu-G (GA-G for short) family of distributions, and with a certain restriction on the parameter space, the family is shown to be a life-time distribution. The shape of the density function and hazard rate function of the GA-G family is described analytically. When G follows the Weibull distribution, the generalized Ampadu-Weibull (GA-W for short) is presented along with its hazard and survival function. Several sub-models of the GA-W family are presented. The transformation technique is applied to this new family of distributions, and we obtain the quantile function of the new family. Power series representations for the cumulative distribution function (CDF) and probability density function (PDF) are also obtained. The rth non-central moments, moment generating function, and Renyi entropy associated with the new family of distributions are derived. Characterization theorems based on two truncated moments and conditional expectation are also presented. A simulation study is also conducted, and we find that using the method of maximum likelihood to estimate model parameters is adequate. The GA-W family of distributions is shown to be practically significant in modeling real life data, and is shown to be superior to some non-trivial generalizations of the Weibull distribution. A further development concludes the paper.

scholarly journals The chaos in calibrating crop models

2020 ◽  
Author(s):  
Daniel Wallach ◽  
Taru Palosuo ◽  
Peter Thorburn ◽  
Zvi Hochman ◽  
Emmanuelle Gourdain ◽  
...  
Keyword(s):  
Experimental Data ◽  
Model Calibration ◽  
Crop Model ◽  
Process Models ◽  
Model Parameters ◽  
Model Structure ◽  
Crop Models ◽  
Estimation Of Model Parameters ◽  
Parameter Values ◽  
Made In

Calibration, that is the estimation of model parameters based on fitting the model to experimental data, is among the first steps in essentially every application of crop models and process models in other fields and has an important impact on simulated values. The goal of this study is to develop a comprehensive list of the decisions involved in calibration and to identify the range of choices made in practice, as groundwork for developing guidelines for crop model calibration starting with phenology. Three groups of decisions are identified; the criterion for choosing the parameter values, the choice of parameters to estimate and numerical aspects of parameter estimation. It is found that in practice there is a large diversity of choices for every decision, even among modeling groups using the same model structure. These findings are relevant to process models in other fields.

scholarly journals Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

2021 ◽  
Vol 10 (3) ◽  
pp. 8
Author(s):  
Adebisi Ade Ogunde ◽  
Gbenga Adelekan Olalude ◽  
Oyebimpe Emmanuel Adeniji ◽  
Kayode Balogun
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Maximum Likelihood Method ◽  
Life Time ◽  
Real Data ◽  
Likelihood Method ◽  
Strength Parameter ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data

A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.

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.

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