scholarly journals A Two Parameters Rani Distribution: Estimation and Tests for Right Censoring Data with an Application

2021 ◽  
pp. 1037-1049
Author(s):  
Amer Ibrahim Al-Omari ◽  
Khaoula Aidi ◽  
Nacira Seddik-Ameur
Keyword(s):  
Hazard Function ◽  
Goodness Of Fit ◽  
Reliability Function ◽  
Parameters Estimation ◽  
Right Censoring ◽  
Likelihood Method ◽  
Model Parameters ◽  
Right Censored Data ◽  
Two Parameters ◽  
Reversed Hazard Function

In this paper, we developed a new distribution, namely the two parameters Rani distribution (TPRD). Some statistical properties of the proposed distribution are derived including the moments, moment-generating function, reliability function, hazard function, reversed hazard function, odds function, the density function of order statistics, stochastically ordering, and the entropies. The maximum likelihood method is used for model parameters estimation. Following the same approach suggested by Bagdonavicius and Nikulin (2011), modified chi squared goodness-of-fit tests are constructed for right censored data and some tests for right data is considered. An application study is presented to illustrate the ability of the suggested model in fitting aluminum reduction cells sets and the strength data of glass of the aircraft window.

scholarly journals Estimation of baseflow parameters of variable infiltration capacity model with soil and topography properties for predictions in ungauged basins

2011 ◽  
Vol 8 (4) ◽  
pp. 7017-7053 ◽  
Author(s):  
Z. Bao ◽  
J. Liu ◽  
J. Zhang ◽  
G. Fu ◽  
G. Wang ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Model Simulation ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Ungauged Basins ◽  
Variable Infiltration Capacity ◽  
Infiltration Capacity ◽  
Ungauged Catchments ◽  
Vic Model ◽  
Predictions In Ungauged Basins

Abstract. Equifinality is unavoidable when transferring model parameters from gauged catchments to ungauged catchments for predictions in ungauged basins (PUB). A framework for estimating the three baseflow parameters of variable infiltration capacity (VIC) model, directly with soil and topography properties is presented. When the new parameters setting methodology is used, the number of parameters needing to be calibrated is reduced from six to three, that leads to a decrease of equifinality and uncertainty. This is validated by Monte Carlo simulations in 24 hydro-climatic catchments in China. Using the new parameters estimation approach, model parameters become more sensitive and the extent of parameters space will be smaller when a threshold of goodness-of-fit is given. That means the parameters uncertainty is reduced with the new parameters setting methodology. In addition, the uncertainty of model simulation is estimated by the generalised likelihood uncertainty estimation (GLUE) methodology. The results indicate that the uncertainty of streamflow simulations, i.e., confidence interval, is lower with the new parameters estimation methodology compared to that used by original calibration methodology. The new baseflow parameters estimation framework could be applied in VIC model and other appropriate models for PUB.

scholarly journals A Non-Mixture Cure Model for Right Censored Data with Fréchet Distribution

2018 ◽  
Author(s):  
Durga Kutal ◽  
Lianfen Qian
Keyword(s):  
Censored Data ◽  
Real Data ◽  
Phase Iii ◽  
Likelihood Method ◽  
Model Parameters ◽  
Exponential Distributions ◽  
Right Censored Data ◽  
Cure Model ◽  
Mixture Cure Model ◽  
Allogeneic Marrow

This paper considers a non-mixture cure model for right censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Comparing with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

scholarly journals Testing Procedure for Item Response Probabilities of 2Class Latent Model

2020 ◽  
Vol 39 (3) ◽  
pp. 657-667
Author(s):  
Bushra Shamshad ◽  
Junaid Sagheer Siddiqui
Keyword(s):  
Item Response ◽  
Latent Variable ◽  
Goodness Of Fit ◽  
Latent Class ◽  
Latent Class Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Estimation Of Parameters ◽  
Goodness Of Fit Test ◽  
Significant Difference

This paper presents Hotelling T2 as a procedure for the testing of significance difference between the item response probabilities (ωij′s) of classes in a Latent Class Model (LCM). Parametric bootstrap technique is used in order to generate samples for ωij′s. These samples are based on the estimated parameters of 2-class latent model. The estimation of parameters in either situation is done using the Expectation Maximization (EM) algorithm through Maximum likelihood method. The hypothesis under consideration is whether the response probabilities (ωij′s) are equal against each item in both the classes. { H0 : ωi1 = ωi2. against H1 : =ωi1 ≠ ωi2}. If the test exhibits significant difference between response probabilities in both classes, it will be a clear indication of a presence of latent variable. We consider both training and testing data sets to develop the test. In order to apply Hotelling T2 test the basic assumptions of normality and homogeneity of variance are also checked. Chi-square goodness of fit test is used for assessing normal distribution to be good fitted on the hypothesized (bootstrap samples) based on 2-class latent model parameters for each data and Bartlett test to check heterogeneity of variances in ωij′s. Moreover, our procedure produces a minimum standard error of estimates as compared to those obtained through the package in R.Gui environment

scholarly journals Modified generalized marshall-olkin family of distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 18
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Goodness Of Fit Tests ◽  
New Family ◽  
Family Of Distributions

In this article, we propose a new family of distributions using the T-X family named as modified generalized Marshall-Olkin family of distributions. Comprehensive mathematical and statistical properties of this family of distributions are provided. The model parameters are estimated by maximum likelihood method. The maximum likelihood estimation under Type-II censoring is also discussed. Two lifetime data sets are used to show the suitability and applicability of the new family of distributions. For comparison purposes, different goodness of fit tests are used.  

scholarly journals A New One-parameter G Family of Compound Distributions: Copulas, Statistical Properties and Applications

2021 ◽  
Vol 9 (4) ◽  
pp. 942-962
Author(s):  
Mohamed Abo Raya
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Heavy Tail ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
New Family

This work introduces a new one-parameter compound G family. Relevant statistical properties are derived. The new density can be “asymmetric right skewed with one peak and a heavy tail”, “symmetric” and “left skewedwith one peak”. The new hazard function can be “upside-down”, “upside-down-constant”, “increasing”, “decreasing” and “decreasing-constant”. Many bivariate types have been also derived via different common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and flexibility of the new family is illustrated by means of two real data sets.

scholarly journals Estimating Proportional Hazards Model Using Frequentist and Bayesian Approaches

2014 ◽  
Vol 8 (2) ◽  
Author(s):  
Noraslinda Mohamed Ismail ◽  
Zarina Mohd Khalid ◽  
Norhaiza Ahmad
Keyword(s):  
Bayesian Approach ◽  
Survival Data ◽  
Hazard Function ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Risk Function ◽  
Model Parameters ◽  
Right Censored Data ◽  
Hazards Model ◽  
Leukemia Data

In statistics, the proportional hazards model (PHM) is one of a class of survival models. This model estimates the effects of different covariates influencing the time-to-event data in which the hazard function has been assumed to be the product of the baseline hazard function and a non-negative function of covariates. In this study, we investigate the hazard function, also known as the risk function or intensity function, which is employed in modelling the survival data and waiting times. The model parameters can be estimated via frequentist or Bayesian approach. However, the Bayesian approach is well known to have the advantages over frequentist methods when the data are small in size and involve censored individuals. In this paper, the PHM for right-censored data from Bayesian perspective will be discussed and the Markov Chain Monte Carlo (MCMC) method will be used to estimate the posterior distributions of the model parameters using Leukemia data.

scholarly journals Comparing Different Estimators for the shape Parameter and the Reliability function of Kumaraswamy Distribution

2019 ◽  
Vol 25 (116) ◽  
pp. 199-225
Author(s):  
Jinan Abbas Naser Al-Obedy
Keyword(s):  
Shape Parameter ◽  
Reliability Function ◽  
Bayes Estimation ◽  
Likelihood Method ◽  
Prior Distributions ◽  
Squared Error Loss Function ◽  
Kumaraswamy Distribution ◽  
Chi Squared ◽  
Two Parameters ◽  
Mean Square Errors

In this paper, we used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters l , θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition to that we used method of moments for estimating the parameters of the prior distributions. Bayes estimators derived under the squared error loss function. We conduct simulation study, to compare the performance for each estimator, several values of the shape parameter (θ) from Kumaraswamy distribution for data-generating, for different samples sizes (small, medium, and large). Simulation results have shown that the Best method is the Bayes estimation according to the smallest values of mean square errors(MSE) for all samples sizes (n).  

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 A Non-Mixture Cure Model for Right-Censored Data with Fréchet Distribution

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 176-188 ◽  
Author(s):  
Durga Kutal ◽  
Lianfen Qian
Keyword(s):  
Censored Data ◽  
Real Data ◽  
Phase Iii ◽  
Likelihood Method ◽  
Model Parameters ◽  
Right Censored Data ◽  
Cure Model ◽  
Mixture Cure Model ◽  
Fréchet Distribution ◽  
Frechet Distribution

This paper considers a non-mixture cure model for right-censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Compared with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

scholarly journals Bivariate exponentiated discrete Weibull distribution: statistical properties, estimation, simulation and applications

2019 ◽  
Vol 14 (1) ◽  
pp. 29-42 ◽  
Author(s):  
M. El- Morshedy ◽  
M. S. Eliwa ◽  
A. El-Gohary ◽  
A. A. Khalil
Keyword(s):  
Weibull Distribution ◽  
Joint Probability ◽  
Discrete Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Model Parameters ◽  
Probability Mass Function

AbstractIn this paper, a new bivariate discrete distribution is defined and studied in-detail, in the so-called the bivariate exponentiated discrete Weibull distribution. Several of its statistical properties including the joint cumulative distribution function, joint probability mass function, joint hazard rate function, joint moment generating function, mathematical expectation and reliability function for stress–strength model are derived. Its marginals are exponentiated discrete Weibull distributions. Hence, these marginals can be used to analyze the hazard rates in the discrete cases. The model parameters are estimated using the maximum likelihood method. Simulation study is performed to discuss the bias and mean square error of the estimators. Finally, two real data sets are analyzed to illustrate the flexibility of the proposed model.

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