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Articles 1 - 19 of 19
Full-Text Articles in Statistics and Probability
Parameter Estimation Based On Double Ranked Set Samples With Applications To Weibull Distribution, Mohamed Abd Elhamed Sabry, Hiba Zeyada Muhammed, Mostafa Shaaban, Abd El Hady Nabih
Parameter Estimation Based On Double Ranked Set Samples With Applications To Weibull Distribution, Mohamed Abd Elhamed Sabry, Hiba Zeyada Muhammed, Mostafa Shaaban, Abd El Hady Nabih
Journal of Modern Applied Statistical Methods
In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating …
On The Extension Of Exponentiated Pareto Distribution, Amal S. Hassan, Saeed Elsayed Hemeda, Said G. Nassr
On The Extension Of Exponentiated Pareto Distribution, Amal S. Hassan, Saeed Elsayed Hemeda, Said G. Nassr
Journal of Modern Applied Statistical Methods
In this study, an extended exponentiated Pareto distribution is proposed. Some statistical properties are derived. We consider maximum likelihood, least squares, weighted least squares and Bayesian estimators. A simulation study is implemented for investigating the accuracy of different estimators. An application of the proposed distribution to a real data is presented.
A New Generating Family Of Distributions: Properties And Applications To The Weibull Exponential Model, El-Sayed A. El-Sherpieny, Salwa Assar, Tamer Helal
A New Generating Family Of Distributions: Properties And Applications To The Weibull Exponential Model, El-Sayed A. El-Sherpieny, Salwa Assar, Tamer Helal
Journal of Modern Applied Statistical Methods
A new method for generating family of distributions was proposed. Some fundamental properties of the new proposed family include the quantile, survival function, hazard rate function, reversed hazard and cumulative hazard rate functions are provided. This family contains several new models as sub models, such as the Weibull exponential model which was defined and discussed its properties. The maximum likelihood method of estimation is using to estimate the model parameters of the new proposed family. The flexibility and the importance of the Weibull-exponential model is assessed by applying it to a real data set and comparing it with other known …
Extending Singh-Maddala Distribution, Mohamed Ali Ahmed
Extending Singh-Maddala Distribution, Mohamed Ali Ahmed
Journal of Modern Applied Statistical Methods
A new distribution, the exponentiated transmuted Singh-Maddala distribution (ETSM), is presented, and three important special distributions are illustrated. Some mathematical properties are obtained, and parameters estimation method is applied using maximum likelihood. Illustrations based on random numbers and a real data set are given.
Maximum Likelihood Estimation For The Generalized Pareto Distribution And Goodness-Of-Fit Test With Censored Data, Minh H. Pham, Chris Tsokos, Bong-Jin Choi
Maximum Likelihood Estimation For The Generalized Pareto Distribution And Goodness-Of-Fit Test With Censored Data, Minh H. Pham, Chris Tsokos, Bong-Jin Choi
Journal of Modern Applied Statistical Methods
The generalized Pareto distribution (GPD) is a flexible parametric model commonly used in financial modeling. Maximum likelihood estimation (MLE) of the GPD was proposed by Grimshaw (1993). Maximum likelihood estimation of the GPD for censored data is developed, and a goodness-of-fit test is constructed to verify an MLE algorithm in R and to support the model-validation step. The algorithms were composed in R. Grimshaw’s algorithm outperforms functions available in the R package ‘gPdtest’. A simulation study showed the MLE method for censored data and the goodness-of-fit test are both reliable.
An Extended Weighted Exponential Distribution, Abbas Mahdavi, Leila Jabari
An Extended Weighted Exponential Distribution, Abbas Mahdavi, Leila Jabari
Journal of Modern Applied Statistical Methods
A new class of weighted distributions is proposed by incorporating an extended exponential distribution in Azzalini’s (1985) method. Several statistics and reliability properties of this new class of distribution are obtained. Maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms; they have to be obtained by solving some numerical methods. Two data sets are analyzed for illustrative purposes, and show that the proposed model can be used effectively in analyzing real data.
E-Bayesian Estimation Of The Parameter Of The Logarithmic Series Distribution, Parviz Nasiri, Hassan Esfandyarifar
E-Bayesian Estimation Of The Parameter Of The Logarithmic Series Distribution, Parviz Nasiri, Hassan Esfandyarifar
Journal of Modern Applied Statistical Methods
E-Bayesian estimation is introduced to estimate the parameter of logarithmic series distribution. In addition, E-Bayesian, Bayesian and maximum likelihood estimation with through applying mean squared error.
The Xgamma Distribution: Statistical Properties And Application, Subhradev Sen, Sudhansu S. Maiti, N. Chandra
The Xgamma Distribution: Statistical Properties And Application, Subhradev Sen, Sudhansu S. Maiti, N. Chandra
Journal of Modern Applied Statistical Methods
A new probability distribution, the xgamma distribution, is proposed and studied. The distribution is generated as a special finite mixture of exponential and gamma distributions and hence the name proposed. Various mathematical, structural, and survival properties of the xgamma distribution are derived, and it is found that in many cases the xgamma has more flexibility than the exponential distribution. To evaluate the comparative behavior, stochastic ordering of the distribution is studied. To estimate the model parameter, the method of moment and the method of maximum likelihood estimation are proposed. A simulation algorithm to generate random samples from the xgamma distribution …
Some Methods Of Estimation From Censored Samples In Exponential And Gamma Models, R R. L Kantam, B Sriram
Some Methods Of Estimation From Censored Samples In Exponential And Gamma Models, R R. L Kantam, B Sriram
Journal of Modern Applied Statistical Methods
Two popular life testing models exponential and one where its generalization is gamma are considered. Estimation of scale parameter from a general Type-II doubly censored sample is attempted by the principle of maximum likelihood method. Resulting equations found to be giving iterative solutions. As an alternative to iterative solution certain admissible modifications to the estimating equations are suggested in special cases. The resulting estimates are compared with the exact maximum likelihood estimates analytically or through simulation. The results are also extended for reliability estimation.
Gumbel-Weibull Distribution: Properties And Applications, Raid Al-Aqtash, Carl Lee, Felix Famoye
Gumbel-Weibull Distribution: Properties And Applications, Raid Al-Aqtash, Carl Lee, Felix Famoye
Journal of Modern Applied Statistical Methods
Some properties of the Gumbel-Weibull distribution including the mean deviations and modes are studied. A detailed discussion of regions of unimodality and bimodality is given. The method of maximum likelihood is proposed for estimating the distribution parameters and a simulation is conducted to study the performance of the method. Three tests are given for testing the significance of a distribution parameter. The applications of Gumbel-Weibull distribution are emphasized. Five data sets are used to illustrate the flexibility of the distribution in fitting unimodal and bimodal data sets.
On The Exponentiated Weibull Distribution For Modeling Wind Speed In South Western Nigeria, Olanrewaju I. Shittu, K A. Adepoju
On The Exponentiated Weibull Distribution For Modeling Wind Speed In South Western Nigeria, Olanrewaju I. Shittu, K A. Adepoju
Journal of Modern Applied Statistical Methods
One of the bases for assessment of wind energy potential for a specified region is the probability distribution of wind speed. Thus, appropriate and adequate specification of the probability distribution of wind speed becomes increasingly important. Several distributions have been proposed for describing wind distribution. Among the most popular distributions is the Weibull whose choice is due to its flexibility. An exponentiated Weibull distribution is proposed as an alternative to model wind speed data with a view to comparing it with the existing Weibull distribution. Results indicate that the proposed distribution outperforms the existing Weibull distribution for modeling wind speed …
Comparison Of Parameters Of Lognormal Distribution Based On The Classical And Posterior Estimates, Raja Sultan, S. P. Ahmad
Comparison Of Parameters Of Lognormal Distribution Based On The Classical And Posterior Estimates, Raja Sultan, S. P. Ahmad
Journal of Modern Applied Statistical Methods
Lognormal distribution is widely used in scientific field, such as agricultural, entomological, biology etc. If a variable can be thought as the multiplicative product of some positive independent random variables, then it could be modelled as lognormal. In this study, maximum likelihood estimates and posterior estimates of the parameters of lognormal distribution are obtained and using these estimates we calculate the point estimates of mean and variance for making comparisons.
Parameter Estimations Based On Kumaraswamy Progressive Type Ii Censored Data With Random Removals, Navid Feroze, Ibrahim El-Batal
Parameter Estimations Based On Kumaraswamy Progressive Type Ii Censored Data With Random Removals, Navid Feroze, Ibrahim El-Batal
Journal of Modern Applied Statistical Methods
The estimation of two parameters of the Kumaraswamy distribution is considered under Type II progressive censoring with random removals, where the number of units removed at each failure time has a binomial distribution. The MLE was used to obtain the estimators of the unknown parameters, and the asymptotic variance - covariance matrix was also obtained. The formula to compute the expected test time was derived. A numerical study was carried out for different combinations of model parameters. Different censoring schemes were used for the estimation, and performance of these schemes was compared.
Parameter Estimation With Mixture Item Response Theory Models: A Monte Carlo Comparison Of Maximum Likelihood And Bayesian Methods, W. Holmes Finch, Brian F. French
Parameter Estimation With Mixture Item Response Theory Models: A Monte Carlo Comparison Of Maximum Likelihood And Bayesian Methods, W. Holmes Finch, Brian F. French
Journal of Modern Applied Statistical Methods
The Mixture Item Response Theory (MixIRT) can be used to identify latent classes of examinees in data as well as to estimate item parameters such as difficulty and discrimination for each of the groups. Parameter estimation via maximum likelihood (MLE) and Bayesian estimation based on the Markov Chain Monte Carlo (MCMC) are compared for classification accuracy and parameter estimation bias for difficulty and discrimination. Standard error magnitude and coverage rates were compared across number of items, number of latent groups, group size ratio, total sample size and underlying item response model. Results show that MCMC provides more accurate group membership …
Statistical Inferences For Lomax Distribution Based On Record Values (Bayesian And Classical), Parviz Nasiri, Saman Hosseini
Statistical Inferences For Lomax Distribution Based On Record Values (Bayesian And Classical), Parviz Nasiri, Saman Hosseini
Journal of Modern Applied Statistical Methods
A maximum likelihood estimation (MLE) based on records is obtained and a proper prior distribution to attain a Bayes estimation (both informative and non-informative) based on records for quadratic loss and squared error loss functions is also calculated. The study considers the shortest confidence interval and Highest Posterior Distribution confidence interval based on records, and using Mean Square Error MSE criteria for point estimation and length criteria for interval estimation, their appropriateness to each other is examined.
Estimating The Parameters Of Rayleigh Cumulative Exposure Model In Simple Step-Stress Testing. Natasha Beretvas Is An, Mohammed Al-Haj Ebrahem, Abedel-Qader Al-Masri
Estimating The Parameters Of Rayleigh Cumulative Exposure Model In Simple Step-Stress Testing. Natasha Beretvas Is An, Mohammed Al-Haj Ebrahem, Abedel-Qader Al-Masri
Journal of Modern Applied Statistical Methods
Assumes the life distribution of a test unit for any stress follows a Rayleigh distribution with scale parameterθ , and that Ln(θ ) is a linear function of the stress level. Maximum likelihood estimators of the parameters under a cumulative exposure model are obtained. The approximate variance estimates obtained from the asymptotic normal distribution of the maximum likelihood estimators are used to construct confidence intervals for the model parameters. A simulation study was conducted to study the performance of the estimators. Simulation results showed that in terms of bias, mean squared error, attainment of the nominal confidence level, symmetry …
The Construction And Analysis Of Adaptive Group Sequential Designs, Mark J. Van Der Laan
The Construction And Analysis Of Adaptive Group Sequential Designs, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In order to answer scientific questions of interest one often carries out an ordered sequence of experiments generating the appropriate data over time. The design of each experiment involves making various decisions such as 1) What variables to measure on the randomly sampled experimental unit?, 2) How regularly to monitor the unit, and for how long?, 3) How to randomly assign a treatment or drug-dose to the unit?, among others. That is, the design of each experiment involves selecting a so called treatment mechanism/monitoring mechanism/ missingness/censoring mechanism, where these mechanisms represent a formally defined conditional distribution of one of these …
The Cross-Validated Adaptive Epsilon-Net Estimator, Mark J. Van Der Laan, Sandrine Dudoit, Aad W. Van Der Vaart
The Cross-Validated Adaptive Epsilon-Net Estimator, Mark J. Van Der Laan, Sandrine Dudoit, Aad W. Van Der Vaart
U.C. Berkeley Division of Biostatistics Working Paper Series
Suppose that we observe a sample of independent and identically distributed realizations of a random variable. Assume that the parameter of interest can be defined as the minimizer, over a suitably defined parameter space, of the expectation (with respect to the distribution of the random variable) of a particular (loss) function of a candidate parameter value and the random variable. Examples of commonly used loss functions are the squared error loss function in regression and the negative log-density loss function in density estimation. Minimizing the empirical risk (i.e., the empirical mean of the loss function) over the entire parameter space …
Asymptotic Optimality Of Likelihood Based Cross-Validation, Mark J. Van Der Laan, Sandrine Dudoit, Sunduz Keles
Asymptotic Optimality Of Likelihood Based Cross-Validation, Mark J. Van Der Laan, Sandrine Dudoit, Sunduz Keles
U.C. Berkeley Division of Biostatistics Working Paper Series
Likelihood-based cross-validation is a statistical tool for selecting a density estimate based on n i.i.d. observations from the true density among a collection of candidate density estimators. General examples are the selection of a model indexing a maximum likelihood estimator, and the selection of a bandwidth indexing a nonparametric (e.g. kernel) density estimator. In this article, we establish asymptotic optimality of a general class of likelihood based cross-validation procedures (as indexed by the type of sample splitting used, e.g. V-fold cross-validation), in the sense that the cross-validation selector performs asymptotically as well (w.r.t. to the Kullback-Leibler distance to the true …