scholarly journals A Three-parameter New Exponentiated Distribution for Life-time Data

2020 ◽  
pp. 194-203
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Goodness Of Fit ◽  
Survival Function ◽  
Continuous Distribution ◽  
Life Time ◽  
Least Square ◽  
Cumulative Distribution ◽  
Model Parameters ◽  
Time Data ◽  
Data Set ◽  
Exponentiated Distribution

In the presented work, a continuous distribution consisting of three-parameters is proposed for life-time data called new exponentiated distribution. The discussion of some of the distribution’s statistical as well as mathematical properties, including the Cumulative Distribution Function (CDF), Probability Density function (PDF), quantile function, survival function, hazard rate function, kurtosis measures and skewness, is conducted. The estimation of the presented distribution’s model parameters is performed using the techniques of Cramer-Von-Mises estimation (CVME), least-square estimation (LSE), and maximum likelihood estimation (MLE). The evaluation of the proposed distribution’s goodness of fit is performed through its fitting in comparison with some of the other existing life-time models with the help of a real data set.

scholarly journals THE LOGISTIC INVERSE LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATIONS

2021 ◽  
Vol 09 (01) ◽  
Author(s):  
Ramesh Kumar Joshi ◽  
Keyword(s):  
Goodness Of Fit ◽  
Survival Function ◽  
Continuous Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution

In this article, a three-parameter continuous distribution is introduced called Logistic inverse Lomax distribution. We have discussed some mathematical and statistical properties of the distribution such as the probability density function, cumulative distribution function and hazard rate function, survival function, quantile function, the skewness, and kurtosis measures. The model parameters of the proposed distribution are estimated using three well-known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. The goodness of fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real data set.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

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 Statistical inferences with jointly type-II censored samples from two Pareto distributions

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 557-565 ◽  
Author(s):  
Hanaa H. Abu-Zinadah
Keyword(s):  
Confidence Intervals ◽  
Life Time ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data ◽  
Data Set ◽  
Censored Samples ◽  
Credible Intervals ◽  
Life Tests ◽  
Censoring Scheme

AbstractIn the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

scholarly journals Polynomial Load Model Development for Analysing Residential Electric Energy Use Behaviour

2018 ◽  
Vol 218 ◽  
pp. 01007 ◽  
Author(s):  
Erwin Nashrullah ◽  
Abdul Halim
Keyword(s):  
Energy Use ◽  
Mean Squared Error ◽  
Median Filter ◽  
Energy System ◽  
Least Square ◽  
Model Parameters ◽  
Data Sampling ◽  
Data Set ◽  
System Designer ◽  
Load Model

Analysing and simulating the dynamic behaviour of home power system as a part of community-based energy system needs load model of either aggregate or dis-aggregate power use. Moreover, in the context of home energy efficiency, development of specific and accurate residential load model can help system designer to develop a tool for reducing energy consumption effectively. In this paper, a new method for developing two types of residential polynomial load model is presented. In the research, computation technique of model parameters is provided based on median filter and least square estimation and implemented by MATLAB. We use AMPDs data set, which have 1-minute data sampling, to show the effectiveness of proposed method. After simulation is carried out, the performance evaluation of model is provided through exploring root mean-squared error between original data and model output. From simulation results, it could be concluded that proposed model is enough for helping system designer to analyse home power energy use.

scholarly journals Cure fraction models using mixture and non-mixture models

2012 ◽  
Vol 51 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Jorge A. Achcar ◽  
Emílio A. Coelho-Barros ◽  
Josmar Mazucheli
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Mixture Models ◽  
Censored Data ◽  
Life Time ◽  
Time Data ◽  
Data Set ◽  
Cure Fraction ◽  
The Bayesian Approach

ABSTRACT We introduce the Weibull distributions in presence of cure fraction, censored data and covariates. Two models are explored in this paper: mixture and non-mixture models. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a life- time data set.

scholarly journals HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

2020 ◽  
pp. 276-287
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Type I ◽  
Data Set ◽  
Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

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 Inverted Power Rama Distribution with Applications to Life Time Data

2020 ◽  
pp. 1-21
Author(s):  
Chrisogonus K. Onyekwere ◽  
George A. Osuji ◽  
Samuel U. Enogwe
Keyword(s):  
Heavy Tails ◽  
Survival Function ◽  
Real Life ◽  
Stochastic Ordering ◽  
Life Time ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Statistical Characteristics ◽  
Entropy Measure ◽  
Time Data

In this paper, we introduced the Inverted Power Rama distribution as an extension of the Inverted Rama distribution. This new distribution is capable of modeling real life data with upside down bathtub shape and heavy tails. Mathematical and statistical characteristics such as the quantile function, mode, moments and moment generating function, entropy measure, stochastic ordering and distribution of order statistics have been derived. Furthermore, reliability measures like survival function, hazard function and odds function have been derived. The method of maximum likelihood was used for estimating the parameters of the distribution. To demonstrate the applicability of the distribution, a numerical example was given. Based on the results, the proposed distribution performed better than the competing distributions.

scholarly journals Different Classical Methods of Estimation and Chi-squared Goodness-of-fit Test for Unit Generalized Inverse Weibull Distribution

2021 ◽  
Vol 50 (5) ◽  
pp. 77-100
Author(s):  
Aidi khaoula ◽  
Sanku Dey ◽  
Devendra Kumar ◽  
Seddik-Ameur N
Keyword(s):  
Weibull Distribution ◽  
Simulation Study ◽  
Goodness Of Fit ◽  
Generalized Inverse ◽  
Real Data ◽  
Least Square ◽  
Data Set ◽  
Inverse Weibull Distribution ◽  
Chi Squared ◽  
New Distribution

In this paper, we try to contribute to the distribution theory literature by incorporating a new bounded distribution, called the unit generalized inverse Weibull distribution (UGIWD) in the (0, 1) intervals by transformation method. The proposed distribution exhibits  increasing and bathtub shaped hazard rate function. We derive some basic statistical properties of the new distribution. Based on complete sample, the model parameters are obtained by the methods of maximum likelihood, least square, weighted least square, percentile, maximum product of spacing and Cram`er-von-Mises and compared them using Monte Carlo simulation study. In addition, bootstrap confidence intervals of the parameters of the model based on aforementioned methods of estimation are also obtained. We illustrate the performance of the proposed distribution by means of one real data set and the data set shows that the new distribution is more appropriate as compared to unit Birnbaum-Saunders, unit gamma, unit Weibull, Kumaraswamy and unit Burr III distributions. Further, we construct chi-squared goodness-of-fit tests for the UGIWD using right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modification. The criterion test used is the modified chi-squared statistic Y^2, developedby Bagdonavi?ius and Nikulin, 2011 for some parametric models when data are censored. The performances of the proposed test are shown by an intensive simulation study and an application to real data set

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