Statistics and Probability Commons^™

(R2152) New Bivariate Type-2 Gumbel Distribution Based On The Farlie-Gumbel-Morgenstern Copula: Properties And Its Application In Survival Analysis, Muneeb Javed, Said Farooq Shah, Muhammad Osama, Muhammad Atif, Muhammad Farooq

Applications and Applied Mathematics: An International Journal (AAM)

We introduce a new bivariate probability distribution, termed the Bivariate FGM Type-2 Gumbel Distribution, constructed by combining the Farlie–Gumbel–Morgenstern (FGM) copula with the Type-2 Gumbel marginal distributions. This proposed distribution provides a flexible framework for modeling bivariate data and offers a viable alternative to several existing bivariate distributions, especially in scenarios where capturing dependence between variables is crucial. The theoretical properties of the distribution are thoroughly explored. We derive the marginal and conditional distributions, conditional expectations, moment generating function, and product moments. Procedures for random number generation from the distribution are discussed. Reliability-based characteristics, such as the survival function and …

(R2095) On Discrete Hypoexponential Distribution And Integer-Valued Autoregressive Process, K. Krishnakumari, Dais George

Applications and Applied Mathematics: An International Journal (AAM)

Discrete distributions provide a substantive contribution in modeling real world frame work. Though a lot of discrete distributions are available in literature, they are inappropriate to model many practical situations. The conventional discrete distributions like geometric, Negative Binomial and Poisson have limited applications in modeling count and lifetime data. This paper introduces a new two parameter discrete distribution namely, discrete hypoexponential distribution by discretizing the well known hypoexponential distribution. Various distributional and structural properties of the proposed distribution are studied. We introduce a first order auto regressive process with the newly proposed distribution as marginal and study the properties. Depending …

(R2024) A New Weighted Poisson Distribution For Over- And Under-Dispersion Situations, Michel Koukouatikissa Diafouka, Gelin Chedly Louzayadio, Rodnellin Onéime Malouata

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose a four-parameter weighted Poisson distribution that includes and generalizes the weighted Poisson distribution proposed by Castillo and Pérez-Casany and the Conway- Maxwell-Poisson distribution, as well as other well-known distributions. It is a distribution that is a member of the exponential family and is an exponential combination formulation between the weighted Poisson distribution proposed by Castillo and Pérez-Casany and the Conway-Maxwell- Poisson distribution. This new distribution with an additional parameter of dispersion is more flexible, and the Fisher dispersion index can be greater than, equal to, or less than one. This last property allows it to …

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 …

(R1239) A New Type Ii Half Logistic-G Family Of Distributions With Properties, Regression Models, System Reliability And Applications, Emrah Altun, Morad Alizadeh, Haitham M. Yousof, Mahdi Rasekhi, G. G. Hamedani

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a new family of distributions based on the half logistic distribution. With the new family, the baseline distributions gain flexibility through additional shape parameters. The important statistical properties of the proposed family are derived. A new generalization of the Weibull distribution is used to introduce a location-scale regression model for the censored response variable. The utility of the introduced models is demonstrated in survival analysis and estimation of the system reliability. Three data sets are analyzed. According to the empirical results, it is observed that the proposed family gives better results than other existing models.

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.

Cubic Rank Transmuted Modified Burr Iii Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Seyed Morteza Najibi, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

We propose a lifetime distribution with flexible hazard rate called cubic rank transmuted modified Burr III (CRTMBIII) distribution. We develop the proposed distribution on the basis of the cubic ranking transmutation map. The density function of CRTMBIII is symmetrical, right-skewed, left-skewed, exponential, arc, J and bimodal shaped. The flexible hazard rate of the proposed model can accommodate almost all types of shapes such as unimodal, bimodal, arc, increasing, decreasing, decreasing-increasing-decreasing, inverted bathtub and modified bathtub. To show the importance of proposed model, we present mathematical properties such as moments, incomplete moments, inequality measures, residual life function and stress strength reliability …

Estimation Problems For Pooled Data, Xichen Mou

Theses and Dissertations

In epidemiological applications, individual specimens (e.g., blood, urine, etc.) are often pooled together to detect the presence of disease or to measure the concentration level of a specific biomarker. Due to the advantage of cost efficiency, pooled data are also seen in diverse areas such as genetics, animal ecology, and environmental science. With pooled data, individual observations are masked and new statistical methods are needed to estimate characteristics such as disease prevalence, the underlying density function of a biomarker, etc. We focus on three estimation problems for pooled data. Chapters 2 and 3 propose nonparametric estimators for the density function …

Exploring The Variance Of The Sample Variance Through Estimation And Simulation, Christina Stradwick

Theses, Dissertations and Capstones

In this thesis, we examine properties of the variance of the sample variance, which we will denote V (S ² ). We derive a formula for this variance and show that it only depends on the sample size, variance, and kurtosis of the underlying distribution. We also derive the maximum likelihood estimators for this parameter, V^ˆ (S ² ), under the normal, exponential, Bernoulli, and Poisson distributions and end the thesis with simulations demonstrating the distributions of these estimators.

Strategies To Adjust For Response Bias In Clinical Trials: A Simulation Study, Victoria R. Swaidan

USF Tampa Graduate Theses and Dissertations

Background: Response bias can distort treatment effect estimates and inferences in clinical trials. Although prevention, quantification, and adjustments have been developed, current methods are not applicable when subject-level reliability is used as the measure of response bias. Thus, the objective of the current study is to develop, test, and recommend a series of bias correction strategies for use in these cases. Methods: Monte Carlo simulation and logistic regression modeling were used to develop the strategies, examining the collective impact of sample size (N), effect size (ES), reliability distribution, and response style on estimating the treatment effect size in a series …

Dimension Reduction For Classification With Many Covariates And Pathway Activity Level Estimation, Seungchul Baek

Theses and Dissertations

The development of science and technology has enabled the use of more covariates. As a result, it has become more difficult to identify dependencies among many covariates. Dimension reduction provides an efficient way to handle this issue by summarizing the effect of covariates via a few linear combinations of covariates. In this dissertation, two methodologies for real-life problems are provided by using dimension reduction equipped with semiparametric theory. The use of semiparametrics allows maximal flexibility of the model by letting some features of the model completely unspecified, while we still enjoy the interpretability of the model through estimating the parameters …

Semiparametric Statistical Estimation And Inference With Latent Information, Qianqian Wang

Theses and Dissertations

In Chapter 1, we predicted disease risk by transformation models in the presence of missing subgroup identifiers. When a discrete covariate defining subgroup membership is missing for some of the subjects in a study, the distribution of the outcome follows a mixture distribution of the subgroup-specific distributions. Taking into account the uncertain distribution of the group membership and the covariates, we model the relation between the disease onset time and the covariates through transformation models in each sub-population, and develop a nonparametric maximum likelihood based estimation implemented through EM algorithm along with its inference procedure. We further propose methods to …

Juvenile Remains: Predicting Body Mass And Stature In Modern American Populations, Erin F E Pinkston

Cal Poly Humboldt theses and projects

There are increasing numbers of unidentified persons in the U.S. and abroad. To generate positive identifications, forensic anthropologists and others working in the medicolegal field employ a variety of methods to produce biological profiles to match to case files and missing persons databases. Body mass, and stature are two important components of a biological profile, and both can be estimated using regression formulae derived from skeletal metrics. In cases of unidentified juvenile remains, these are particularly important metrics, as it is difficult or impossible to determine sex in prepubescent remains, and the quality of ancestry estimation is currently under debate …

Sample Size Estimation For Linear Mixed Models With Dependent End Points, Michael Nsiah-Nimo

Open Access Theses & Dissertations

The primary objective is sample size estimation in linear mixed model settings. Sample size estimation is an important component of planning a well thought out scientific experiment. Whenever sample size estimation is performed, taking into account a priori model based inferences will provide a sample size estimate that will achieve the desired power without inflating the type I error rate of the study.

One common practice is a traditional approach cited in the literature that uses the largest sample size after you Bonferroni the type I error rate to estimate sample sizes as such. We are going to take into …

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 …

Measurement Error Estimation Methods In Survey Methodology, Alireza Zahedian, Roshanak A. Saba

Applications and Applied Mathematics: An International Journal (AAM)

One of the most important topics that are discussed in survey methodology is the accuracy of statistics or survey errors that may occur in the parameters estimation process. In statistical literature, these errors are grouped into two main categories: sampling errors and non-sampling errors. Measurement error is one of the most important non-sampling errors. Since estimating of measurement error is more complex than other types of survey errors, much more research has been done on ways of preventing or dealing with this error. The main problem associated with measurement error is the difficulty to measure or estimate this error in …

The Kumaraswamy Marshal-Olkin Family Of Distributions, Morad Alizadeh, M. H. Tahir, Gauss M. Cordeiro, M. Mansoor, Muhammad Zubair, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. The method of maximum …

Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation, Araz Ryan Hashemi

Wayne State University Dissertations

This dissertation investigates problems arising in identification and control of stochastic systems. When the parameters determining the underlying systems are unknown and/or time varying, estimation and adaptive filter- ing are invoked to to identify parameters or to track time-varying systems. We begin by considering linear systems whose coefficients evolve as a slowly- varying Markov Chain. We propose three families of constant step-size (or gain size) algorithms for estimating and tracking the coefficient parameter: Least-Mean Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms.

The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of …

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.

An Evaluation Of Inferential Procedures For Adaptive Clinical Trial Designs With Pre-Specified Rules For Modifying The Sample Size, Greg P. Levin, Sarah C. Emerson, Scott S. Emerson

UW Biostatistics Working Paper Series

Many papers have introduced adaptive clinical trial methods that allow modifications to the sample size based on interim estimates of treatment effect. There has been extensive commentary on type I error control and efficiency considerations, but little research on estimation after an adaptive hypothesis test. We evaluate the reliability and precision of different inferential procedures in the presence of an adaptive design with pre-specified rules for modifying the sampling plan. We extend group sequential orderings of the outcome space based on the stage at stopping, likelihood ratio test statistic, and sample mean to the adaptive setting in order to compute …

Quantifying Alternative Splicing From Paired-End Rna-Sequencing Data, David Rossell, Camille Stephan-Otto Attolini, Manuel Kroiss, Almond Stöcker

COBRA Preprint Series

RNA-sequencing has revolutionized biomedical research and, in particular, our ability to study gene alternative splicing. The problem has important implications for human health, as alternative splicing is involved in malfunctions at the cellular level and multiple diseases. However, the high-dimensional nature of the data and the existence of experimental biases pose serious data analysis challenges. We find that the standard data summaries used to study alternative splicing are severely limited, as they ignore a substantial amount of valuable information. Current data analysis methods are based on such summaries and are hence sub-optimal. Further, they have limited flexibility in accounting for …

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 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

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.

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 …

Water Quality Models For Stormwater Runoff In Two Lincoln, Nebraska Urban Watersheds, Jake Fisher

Department of Civil and Environmental Engineering: Dissertations, Theses, and Student Research

Water quality monitoring was conducted in two urban watersheds (Colonial Hills and Taylor Park) located in southeast Lincoln, NE over a three year period spanning from October 2008 through September 2011. In-line probes continuously measured for turbidity, conductivity, dissolved oxygen, and water temperature while other water quality constituents were analyzed for discrete water samples collected using grab and automatic sampling techniques. The water quality data was used to calculate event mean concentrations (EMCs) for sixteen storm events sampled over the duration of the project period. Three types of stormwater quality multiple linear regression models were developed for the estimation of …

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 …

Statistical Properties Of A Convoluted Beta-Weibull Distribution, Jianan Sun

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. (2002)); beta-Gumbel (Nadarajah and Kotz (2004)); beta-exponential (Nadarajah and Kotz (2006)); beta-Weibull (Famoye et al. (2005)); beta-Rayleigh (Akinsete and Lowe (2008)); beta-Laplace (Kozubowski and Nadarajah (2008)); and beta-Pareto (Akinsete et al. (2008)), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in the literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known …

On The Testing And Estimation Of High-Dimensional Covariance Matrices, Thomas Fisher

All Dissertations

Many applications of modern science involve a large number of parameters. In
many cases, the number of parameters, p, exceeds the number of observations,
N. Classical multivariate statistics are based on the assumption that the
number of parameters is fixed and the number of observations is large. Many of
the classical techniques perform poorly, or are degenerate, in high-dimensional
situations.
In this work, we discuss and develop statistical methods for inference of
data in which the number of parameters exceeds the number of observations.
Specifically we look at the problems of hypothesis testing regarding and the
estimation of the covariance …

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.