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.

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Beta-Burr Type X Distribution with Application to Luteinizing Hormone Data

Beta-Burr Type X distribution is a three parameter distribution and can model right skewed, left skewed, and symmetric data. Beta-Burr Type X distribution is the result of composition distribution functions of beta distribution and Burr Type X distribution. In this study, the characteristics such as probability density function (PDF), cumulative distribution function (CDF), the r-th moment, mean, and variance are presented. The maximum likelihood method is used to estimate the parameters of Beta-Burr Type X distribution, and the solution is obtained using a numerical method. As an illustration, Beta-Burr Type X distribution is used to model the data of luteinizing hormone in female blood samples.

Bayesian Method for Hurdle Regression

Hurdle model is an alternative model to overcome overdispersion caused by excess zero. The model consists of two stages: a binary process that determines whether the response variable has zero values or positive values, and the second stage to model only the positive counts. The first stage is modelled using binary logistic regression, and the next stage is modeled with the zero-truncated model using Poisson regression. Bayesian method was employed to estimate the models’ parameters. Non-informative priors were specified for the parameters, and combined with the likelihood from the data, the non-closed form of posterior distributions were obtained, thus leading to the use of Markov Chain Monte Carlo (MCMC) with Gibbs Sampling to obtain samples from the posterior distributions. This method was applied to model the frequency of motoric complication in people with Parkinson’s disease. The result showed that subtotal scores from the three parts of Movement Disorder Society-Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) could explain the frequency of motoric complication well, implied by the significance of the regression coefficients.

Identification of New Positive Tuberculosis Cases in Aceh Besar District Using Ordinary Criging

Tuberculosis is a contagious infectious disease caused by Mycobacterium tuberculosis. The risk level of transmission of pulmonary tuberculosis with positive smear of acid-resistant bacteria (BTA). BTA is greater hight risk than pulmonary tuberculosis with negative smear. This study aims to predict areas of the number of new BTA positive tuberculosis cases in Aceh Besar district spatially using the kriging method. The data used are secondary data coordinate the point of the number of new cases of positive smear tuberculosis in each puskesmas in the province of Aceh in 2015-2017. The experimental semivariogram calculation is the first step in estimating using ordinary kriging, which is a reference for getting the parameters to be used in theoretical semivariogram calculations. In this case, the semivariogram suitable for new cases of smear positive tuberculosis is the one of the Spherical model. The sill value used is 126.530, the nugget=62, while the range used is based on the distance of each class = 0.158. The results of the analysis showed that the regions with the lowest positive BTA Tuberculosis prediction cases were around Pulo Aceh Sub-District, Montasik Sub-District, and Indrapuri Sub-District, with less than 15 cases. Whereas the region with the most positive predictions of new cases of BTA Tuberculosis was around Baitussalam Sub-District and Jantho City, with more than 30 cases.