A Review of Constrained Principal Component Analysis (CPCA) with Application on Bootstrap
Issue:
Volume 5, Issue 2, April 2019
Pages:
21-30
Received:
10 August 2019
Accepted:
26 August 2019
Published:
10 September 2019
Abstract: Linear model (LM) provide the advance in regression analysis, where it was considered an important statistical development of the last fifty years, following general linear model (GLM), principal component analysis (PCA) and constrained principal component analysis (CPCA) in the last thirty years. This paper introduce a series of papers prepared within the framework of an international workshop. Firstly, the LM and GLM has been discussed. Next, an overview of PCA has been presented. Then constrained principal component has been shown. Some of its special cases such as PCA, Canonical correlation analysis (CANO), Redundancy analysis (RA), Correspondence analysis (CA), Growth curve models (GCM), Extended growth curve models (ExGCM), Canonical discriminant analysis (CDA), Constrained correspondence analysis, non-symmetric correspondence analysis, Multiple Set CANO, Multiple Correspondence Analysis, Vector Preference Models, Seemingly unrelated regression (SUR), Weighted low rank approximations, Two-Way canonical decomposition with linear constraints, and Multilevel RA has been noted in this paper. Related methods and ordinary least squares (OLS) estimator as a special case form CPCA has been introduced. Finally, an example has been introduced to indicate the importance of CPCA and the different between PCA and CPCA. Where CPCA is a method for structural analysis of multivariate data that combine features of regression analysis and principal component analysis. In this method, the original data first decomposed into several components according to external information. The components then subjected to principal component analysis to explore structures within the components.
Abstract: Linear model (LM) provide the advance in regression analysis, where it was considered an important statistical development of the last fifty years, following general linear model (GLM), principal component analysis (PCA) and constrained principal component analysis (CPCA) in the last thirty years. This paper introduce a series of papers prepared wi...
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On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application
Issue:
Volume 5, Issue 2, April 2019
Pages:
31-36
Received:
9 August 2019
Accepted:
29 August 2019
Published:
16 September 2019
Abstract: Transmutation of baseline distributions has gained popularity in the last decade and many authors have studied the some transmuted distributions such as exponential, Weilbul, gamma, Pareto, normal and many more. This article will focus on the transmutation of type I generalized logistic distribution using quadratic rank transmutation map to develop a transmuted type I generalized logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The graphs of the probability density function (pdf) and cumulative distribution function (cdf) of the model for different values of parameters are illustrated respectively. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted type I generalized logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted type I generalized logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using the model to fit relevant data. The study is concluded by demonstrating the performance of transmuted type I generalized logistic distribution over its parent model.
Abstract: Transmutation of baseline distributions has gained popularity in the last decade and many authors have studied the some transmuted distributions such as exponential, Weilbul, gamma, Pareto, normal and many more. This article will focus on the transmutation of type I generalized logistic distribution using quadratic rank transmutation map to develop...
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