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Articles 1 - 16 of 16
Full-Text Articles in Statistics and Probability
Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, James Jensen
Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, James Jensen
Theses
In this paper we explore Bayesian inference and its application to the problem of estimating the intensity function of a non-homogeneous Poisson process. These processes model the behavior of phenomena in which one or more events, known as arrivals, occur independently of one another over a certain period of time. We are concerned with the number of events occurring during particular time intervals across several realizations of the process. We show that given sufficient data, we are able to construct a piecewise-constant function which accurately estimates the mean rates on particular intervals. Further, we show that as we reduce these …
A New Liu Type Of Estimator For The Restricted Sur Estimator, Kristofer Månsson, B. M. Golam Kibria, Ghazi Shukur
A New Liu Type Of Estimator For The Restricted Sur Estimator, Kristofer Månsson, B. M. Golam Kibria, Ghazi Shukur
Journal of Modern Applied Statistical Methods
A new Liu type of estimator for the seemingly unrelated regression (SUR) models is proposed that may be used when estimating the parameters vector in the presence of multicollinearity if the it is suspected to belong to a linear subspace. The dispersion matrices and the mean squared error (MSE) are derived. The new estimator may have a lower MSE than the traditional estimators. It was shown using simulation techniques the new shrinkage estimator outperforms the commonly used estimators in the presence of multicollinearity.
A Generalization Of The Weibull Distribution With Applications, Maalee Almheidat, Carl Lee, Felix Famoye
A Generalization Of The Weibull Distribution With Applications, Maalee Almheidat, Carl Lee, Felix Famoye
Journal of Modern Applied Statistical Methods
The Lomax-Weibull distribution, a generalization of the Weibull distribution, is characterized by four parameters that describe the shape and scale properties. The distribution is found to be unimodal or bimodal and it can be skewed to the right or left. Results for the non-central moments, limiting behavior, mean deviations, quantile function, and the mode(s) are obtained. The relationships between the parameters and the mean, variance, skewness, and kurtosis are provided. The method of maximum likelihood is proposed for estimating the distribution parameters. The applicability of this distribution to modeling real life data is illustrated by three examples and the results …
A Note On Α-Curvature Of The Manifolds Of The Length-Biased Lognormal And Gamma Distributions In View Of Related Applications In Data Analysis, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
A Note On Α-Curvature Of The Manifolds Of The Length-Biased Lognormal And Gamma Distributions In View Of Related Applications In Data Analysis, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
Journal of Modern Applied Statistical Methods
The α-curvature tensors of the statistical manifolds of the length-biased versions of the log-normal and gamma distributions are derived and discussed. This study was designed to investigate observations related to the parameter estimation for the length-biased lognormal distribution as a model for the lengthbiased data from oil field exploration.
The Length-Biased Lognormal Distribution And Its Application In The Analysis Of Data From Oil Field Exploration Studies, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
The Length-Biased Lognormal Distribution And Its Application In The Analysis Of Data From Oil Field Exploration Studies, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar
Journal of Modern Applied Statistical Methods
The length-biased version of the lognormal distribution and related estimation problems are considered and sized-biased data arising in the exploration of oil fields is analyzed. The properties of the estimators are studied using simulations and the use of sample mode as an estimate of the lognormal parameter is discussed.
Gamma-Pareto Distribution And Its Applications, Ayman Alzaatreh, Felix Famoye, Carl Lee
Gamma-Pareto Distribution And Its Applications, Ayman Alzaatreh, Felix Famoye, Carl Lee
Journal of Modern Applied Statistical Methods
A new distribution, the gamma-Pareto, is defined and studied and various properties of the distribution are obtained. Results for moments, limiting behavior and entropies are provided. The method of maximum likelihood is proposed for estimating the parameters and the distribution is applied to fit three real data sets.
New Approximate Bayesian Confidence Intervals For The Coefficient Of Variation Of A Gaussian Distribution, Vincent A. R. Camara
New Approximate Bayesian Confidence Intervals For The Coefficient Of Variation Of A Gaussian Distribution, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
Confidence intervals are constructed for the coefficient of variation of a Gaussian distribution. Considering the square error and the Higgins-Tsokos loss functions, approximate Bayesian models are derived and compared to a published classical model. The models are shown to have great coverage accuracy. The classical model does not always yield the best confidence intervals; the proposed models often perform better.
The Quotient Of The Beta-Weibull Distribution, Nonhle Channon Mdziniso
The Quotient Of The Beta-Weibull Distribution, Nonhle Channon Mdziniso
Theses, Dissertations and Capstones
A new class of distributions recently developed involves the logit of the beta distribution. Among this class of distributions are, the beta-Normal (Eugene et al. [15]); beta-Gumbel (Nadarajah and Kotz [18]); beta-Exponential (Nadarajah and Kotz [19]); beta-Weibull (Famoye et al. [6]); beta-Rayleigh (Akinsete and Lowe [3]); beta-Laplace (Kozubowshi and Nadarajah [20]); and beta-Pareto (Akinsete et al. [4]), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known …
Estimation Of Parameters Of Johnson’S System Of Distributions, Florence George, K. M. Ramachandran
Estimation Of Parameters Of Johnson’S System Of Distributions, Florence George, K. M. Ramachandran
Journal of Modern Applied Statistical Methods
Fitting distributions to data has a long history and many different procedures have been advocated. Although models like normal, log-normal and gamma lead to a wide variety of distribution shapes, they do not provide the degree of generality that is frequently desirable (Hahn & Shapiro, 1967). To formally represent a set of data by an empirical distribution, Johnson (1949) derived a system of curves with the flexibility to cover a wide variety of shapes. Methods available to estimate the parameters of the Johnson distribution are discussed, and a new approach to estimate the four parameters of the Johnson family is …
Approximate Bayesian Confidence Intervals For The Mean Of A Gaussian Distribution Versus Bayesian Models, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Mean Of A Gaussian Distribution Versus Bayesian Models, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
This study obtained and compared confidence intervals for the mean of a Gaussian distribution. Considering the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the mean of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals were compared to a published Bayesian model. Whereas the published Bayesian method is sensitive to the choice of the hyper-parameters and does not always yield the best confidence intervals, it is shown that the proposed approximate Bayesian approach relies only on the observations and often performs better.
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of this article is to obtain and compare confidence intervals for the mean of an exponential distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for parameters of exponential population are derived. Using exponential data, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with Fisher Matrix bounds method. It is shown that the proposed approximate Bayesian approach relies only on the observations. The Fisher Matrix bounds method, that uses the z-table, does not always yield the best confidence intervals, and the proposed approach often performs better.
Bayesian Reliability Modeling Using Monte Carlo Integration, Vincent A. R. Camara, Chris P. Tsokos
Bayesian Reliability Modeling Using Monte Carlo Integration, Vincent A. R. Camara, Chris P. Tsokos
Journal of Modern Applied Statistical Methods
Bayesian Reliability Modeling Using Monte Carlo IntegrationThe aim of this article is to introduce the concept of Monte Carlo Integration in Bayesian estimation and Bayesian reliability analysis. Using the subject concept, approximate estimates of parameters and reliability functions are obtained for the three-parameter Weibull and the gamma failure models. Four different loss functions are used: square error, Higgins-Tsokos, Harris, and a logarithmic loss function proposed in this article. Relative efficiency is used to compare results obtained under the above mentioned loss functions.
Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan
Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
In van der Laan and Dudoit (2003) we propose and theoretically study a unified loss function based statistical methodology, which provides a road map for estimation and performance assessment. Given a parameter of interest which can be described as the minimizer of the population mean of a loss function, the road map involves as important ingredients cross-validation for estimator selection and minimizing over subsets of basis functions the empirical risk of the subset-specific estimator of the parameter of interest, where the basis functions correspond to a parameterization of a specified subspace of the complete parameter space. In this article we …
Loss-Based Estimation With Cross-Validation: Applications To Microarray Data Analysis And Motif Finding, Sandrine Dudoit, Mark J. Van Der Laan, Sunduz Keles, Annette M. Molinaro, Sandra E. Sinisi, Siew Leng Teng
Loss-Based Estimation With Cross-Validation: Applications To Microarray Data Analysis And Motif Finding, Sandrine Dudoit, Mark J. Van Der Laan, Sunduz Keles, Annette M. Molinaro, Sandra E. Sinisi, Siew Leng Teng
U.C. Berkeley Division of Biostatistics Working Paper Series
Current statistical inference problems in genomic data analysis involve parameter estimation for high-dimensional multivariate distributions, with typically unknown and intricate correlation patterns among variables. Addressing these inference questions satisfactorily requires: (i) an intensive and thorough search of the parameter space to generate good candidate estimators, (ii) an approach for selecting an optimal estimator among these candidates, and (iii) a method for reliably assessing the performance of the resulting estimator. We propose a unified loss-based methodology for estimator construction, selection, and performance assessment with cross-validation. In this approach, the parameter of interest is defined as the risk minimizer for a suitable …
Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of the present study is to obtain and compare confidence intervals for the variance of a Gaussian distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the variance of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with the well known classical method. The Bayesian approach relies only on the observations. It is shown that the proposed approximate Bayesian approach relies only on the observations. The classical method, that uses the Chi-square statistic, does …
Accelerated Hazards Model: Method, Theory And Applications, Ying Qing Chen, Nicholas P. Jewell, Jingrong Yang
Accelerated Hazards Model: Method, Theory And Applications, Ying Qing Chen, Nicholas P. Jewell, Jingrong Yang
U.C. Berkeley Division of Biostatistics Working Paper Series
In an accelerated hazards model, the hazard functions of a failure time are related through the time scale-change, which is often a function of covariates and associated parameters. When the hazard functions have special properties, such as monotonicity in time, the parameters may be clinically meaningful in measuring a treatment effect. This paper reviews methodological and theoretical development of this model. Applications of the accelerated hazards model including sample size calculation in clinical trials, are also explored.