Zero-truncated Poisson-Lindley distribution

In order to find a counting distribution that can handle the condition when the data has no zero-count. Distribution named Zero-truncated Poisson-Lindley distribution is developed. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero-truncated Poisson-Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method. Then, the application of the model to real data is given.

Truncated Spline Estimation of Percentage Poverty Modeling in Papua Province

In estimating the regression curve there are three approaches, namely parametric regression, nonparametric regression and semiparametric regression. Nonparametric regression approach has high flexibility. Nonparametric regression approach that is quite popular is Truncated Spline. Truncated Spline is a polynomial pieces which have segmented and continuous. One of the advantages of Spline is that it can handle data that changes at certain sub intervals, so this model tends to search for data estimates wherever the data pattern moves and there are points of knots. In reality, data patterns often change at certain sub intervals, one of which is data on poverty in the Papua Province. Papua Province is ranked first in the percentage of poor people in Indonesia. The best of model Truncated Spline in nonparametric regression for the poverty model in Papua Province is using a combination of knot.

Cox Piecewise Constant Hazard Model with Bayesian Method

Cox PH model is one of the survival models that is widely used for analyzing time-to-event data. Cox PH model consists of two main components, the baseline hazard consisting of time-dependent component; and the exponential function accomodating explanatory variables. The baseline hazard is not estimated in the Cox PH model, thus not accommodating the need for hazard rate estimation. Therefore, in this paper we discuss the estimation of baseline hazard through piecewise constant hazard using Bayesian method. Gamma distribution is assumed for the piecewise constant baseline hazard, and normal distribution is assumed for the regression coefficient. Sampling from the posterior is conducted using Markov chain Monte Carlo through Gibbs sampling. Echocardiogram data containing 106 observations and 6 explanatory variables were used in analysis. The result showed that the baseline hazard functions were estimated and each of parameters in the model is converged as shown by the trace plot and posterior density plot.

Alpha Power Transformed Lindley Distribution

The one parameter Lindley distribustion (theta) has been widely used in various field such as biology, technique, medical, and industries. Lindley distribution is capable for modelling data with monotone increasing hazard rate. However, in real life, there are situations where the hazard rate is not monotone. Therefore, to enhance the Lindley distribution capabilitiesfor modelling data, a modification can be used by using Alpha Power Transformed method. The result of the modification of Lindley distribution is commonly called Alpha Power Transformed Lindley distribution (APTL) distribution that has two parameters (alpha, theta). This new APTL distribution is appropriate in modelling data with decreasing or unimodal shaped of probability density function, and has hazard rates with increasing, decreasing, and upside-down bathtub shaped. The properties of the proposed distribution are discussed include probability density function, cumulative distribution function, survival function, hazard rate function, moment generating function, and rth moment. Themodel parameters are obtained using maximum likelihood method. The waiting time data is used as an illustration to describe the utility of APTL distribution.

Comparison of Poisson and Quasi-Poisson Regression: A Simulation study

Poisson regression is often used to model count data. However, it requires the assumption of equidispersion which not always met in the real application data. Quasi-Poisson can be considered as an alternative to handle this problem. The objective of this essay is to explain about the Quasi-Poisson regression, the likelihood construction, parameter estimation, and its implementation in real life data. The numerical method used in this study is Newton-Raphson which is equivalent to Iterative Weighted Least Square (IWLS) at the end of calculation. The simulation results for the data with the above problem showed that, in case of overdispersion, Quasi-Poisson regression with Maximum Quasi-Likelihood method provided a good fit to the data compared to Poisson regression.

Preface

Preface

Cover

.

Completeness of P-Summable as Hilbert Space with Its Dual Space

Hilbert space is a complete inner product space, meaning that each Cauchy sequence converges to a point in that space. One of the vector spaces that will be examined as the inner product space is p-summable space. The inner product space is a subset of vector spaces that have special properties that must be fulfilled. One way to prove vector space is the inner product space is to use parallelogram equality theorems. After it is known that the vector space is the inner product space, the completeness of the space will be proven using the dual space. The space used is the p-summable space, data that can be changed in a sequence form will be usable in this study. The results of this study will be useful as another application in determining a Hilbert space by using a method that is different from the definition. The analysis used will show comparison of the speed of completion accuracy will be a benchmark in this study, so that will be a new reference in determining a space is Hilbert space.

Identification of Factors Affecting Tuberculosis in West Java using Spatial Modeling

Tuberculosis (TB) is an infectious disease caused by the bacillus Mycobacterium tuberculosis. In 2017 WHO records there are 1.7 billion TB sufferers in the world. Whereas in the same year TB sufferers in Indonesia reached 421 thousand cases and 10 thousand of them were in the province of West Java. In this study, the factors that suspected to influence TB include poverty, population density and malnutrition were analyzed by looking at the spatial aspects. In addition to these factors, smoking and consuming alcoholic beverages can also trigger TB. The method used was Spatial Autoregressive Model (SARM), Spatial Error Model (SEM), and Generalized Spatial Model (GSM), then the best model is chosen based on the best criteria of lagrange multiplayer test. The result indicated that SEM performed better than others, with the following significant variables were malnutrition and unemployment factor.

Comparison of Poisson and Quasi-Poisson Regression: A Simulation study

Poisson regression is often used to model count data. However, it requires the assumption of equidispersion which not always met in the real application data. Quasi-Poisson can be considered as an alternative to handle this problem. The objective of this essay is to explain about the Quasi-Poisson regression, the likelihood construction, parameter estimation, and its implementation in real life data. The numerical method used in this study is Newton-Raphson which is equivalent to Iterative Weighted Least Square (IWLS) at the end of calculation. The simulation results for the data with the above problem showed that, in case of overdispersion, Quasi-Poisson regression with Maximum Quasi-Likelihood method provided a good fit to the data compared to Poisson regression.