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Sri Lankan Journal of Applied Statistics
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ISSN (Print) 1391-4987
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Shared Frailty Model for Joint Survival Data - A Simulation Study
- Abstract: Performing a survival analysis, allows investigating factors that contribute to outcome over time. Though a considerable amount of literature has addressed this area, analysis of multiple survival responses has not received sufficient attention in past literature. The joint modeling fits well when there are multiple survival responses for the same study unit and it can provide improved results than fitting univariate models separately since the correlation
  between the responses can be captured through a joint model. Therefore, the aim of this study was to propose a joint modeling approach, in which the linkage between two survival responses(for simplicity, in this research bivariate lifetime data have been considered) was derived by sharing a common random effect under different random effect distributions through parametric forms of the baseline hazard function. In this study, Gamma and Normal random effect distributions and Exponential and Weibull parametric survival distributions were considered. The performance of the Shared Frailty model was compared with two Ordinary Proportional Hazard models through a simulation study, by fitting models for simulated data in three different sample sizes with 20% and 40% censoring proportions in different correlation structures. Bias, Coverage Probability (CP) and Mean Squared Error (MSE) were the performance measures used. Parameter estimates showing relatively low bias, high CP, and minimal MSE under the joint random effect model confirmed the suitability of the proposed model to capture joint survival data, surpassing the fit of two univariate models. Also, the results interpreted, Gamma distributed random effects to be more suitable with Exponential survival times while Normal random effects with Weibull survival times. Published on 2022-11-28 00:00:00
Statistical Approach of Identifying Crime Hotspots for GIS Mapping in Sri
Lanka
- Abstract: Currently, crimes are well organized and difficult to investigate, and hence, the situation is more complex due to technological advancements. Therefore, there is a timely need to plan strategies to reduce crime using historical crime data. The objectives of the study are extraction of crime patterns using trend analysis, identifying the relationship between crime and geographic environment, and recognizing the district where crime is most prevalent. Five types of crimes that have a high impact on society from 2010 to 2019 in Sri Lanka were identified using the high mean cluster. There were House Breaking (HB), Hurt by Knife (HK), Robbery (RB), Rape (RP), and Cheating (CH). The result of Shapiro-Wilk test for normality wasn’t normal therefore Kruskal-Wallis multiple comparisons were used. There was a significant difference between the mean of HB, HK, RB, RP, and CH. Using Spearman’s rank correlation coefficient test, a very strong positive correlation was found between RP and HB (0.9472), RB and HB (0.9003) and HK and HB (0.9277). The type of crimes scattered throughout Sri Lanka was analyzed using Geographic Information System (GIS). Thematic maps were generated to identify hotspot areas. The risk of all five types of crime appeared to be high in Kurunegala and Gampaha districts. Prediction Accuracy Index (PAI) values were calculated to compare the predictive accuracy of crime types and the highest PAI value (3.98) was for RB crime. According to the findings of this study, a new security strategy can be developed to eradicate these trends from society. Published on 2022-11-28 00:00:00
Economic Consequences of Population Aging in Sri Lanka
- Abstract: The population aging is unprecedented in human history that brings numerous socio-economic consequences. In this context, this study was with the aim of understanding the impact of population aging on the economic growth of Sri Lanka and the role of the current pension system in Sri Lanka in determining the impact of population aging on economic growth. The study applies a growth accounting framework to evaluate the impacts of population aging on per capita output growth in Sri Lanka, from 1960 - 2019. The Structural Equation Model (SEM) and the dynamic regression with error ARIMA model were used to meet the study’s objectives. The findings revealed that the aging population has a significant negative impact on Sri Lanka’s economic growth, while total factor productivity growth and capital deepening have a favorable impact. Further, Sri Lanka’s present pension system greatly tempered the direct association between population aging and total factor productivity increase. Overall, Sri Lanka’s current pension system exacerbates the negative effects of population aging on economic growth. The findings of the study can be used to draw several policy implications for the planning of welfare and economic development programs in Sri Lanka. Published on 2022-11-28 00:00:00
Unit Gamma/Gompertz Quantile Regression with Applications to Skewed Data
- Abstract: In this study, new unit quantile regression model, called the Unit Gamma/ Gompertz quantile regression for bounded responses is developed by re-parameterizing the Unit Gamma/Gompertz distribution. To estimate the parameters of the new quantile regression model, the maximum likelihood approach is used to develop estimators for the parameters. Monte Carlo simulations are used to test the consistency of the maximum likelihood estimators for the parameters of the new quantile regression model. The application of the new quantile regression model is illustrated using three real life datasets and the results revealed that the Unit Gamma/Gompertz quantile regression performs better than the beta regression model when the unit response variable has skewed observations and outliers. Published on 2022-08-31 03:14:35
ptsuite: Fast Tail Index Estimation for Power Law Distributions in R
- Abstract: Power law distributions, in particular Pareto distributions, describe data across diverse areas of study. We have developed a package, ptsuite, in R to estimate the tail index for such datasets which: a) uses a variety of estimation methods; b) focuses on speed (in particular with large datasets); c) is accurate and d) is easy to use. The package is also able to generate Pareto data as well as conduct both heuristic and statistical tests to check if data is Paretian. We tested ptsuite against similar R packages for speed of tail index estimation and found that our package is indeed faster. The tail index estimates produced by the package are accurate. The package is easy to use as all functions can be called with one line of code and a small number of argument references. To date the package has been downloaded over 12,500 times from the CRAN repository 4. Finally we remark that the authors have used the package in research applications - e.g. (Munasinghe et. al , 2019). Published on 2022-08-31 03:14:29
Modelling Rare Events in an Adaptive Cluster Sampling Design with
Heterogeneity among Networks and within the Network Units
- Abstract: Rare events population (φ) is hard-to-reach, sparsely distributed and clustered; an Adaptive Cluster Sampling (ACS) is the design to collect information from φ. Researchers and Policy Makers have modelled φ in ACS design with homogeneity assumptions. This study modelled φ with heterogeneity among networks and within the network units. Data from the International Institute of Tropical Agriculture on Culcasia Scandens, an understory plant and simulation were used to validate the model. Estimators for total and average number of rare events were derived and their statistical properties were examined. Bayesian Model was embedded in the designed ACS to develop the model for predicting the total number of rare events. Parameters α, β and λ were used in the model to control the expected number of grid cells with rare events, the conditional expected number of sub-network and expected number of rare events in each sub-network respectively. Markov Chain Monte-Carlo Algorithm with R and Winbugs software were used to estimated these parameters. The robustness of the model was examined and its Sensitivity Analysis was carried out. Diagnostic checks were done and the proposed model was compared with the existing model. The samples converged and represented the target posterior and the total number of rare events estimated lies within the 95% HPD credible interval. The derived estimators were unbiased, consistent and efficient. The model was criterion and inference robust with a good fit. The results revealed that rare event was best modelled under heterogeneity assumptions. Published on 2022-08-31 03:14:23
Estimation of Sensitive Variable in Two-Phase Sampling under Measurement
Error And Non-Response Using ORRT Models
- Abstract: In human surveys, people are asked highly confidential questions concerning a sensitive variable. This article concentrate on the estimation of population mean of sensitive variable under two phase sampling using ORRT models. Also, the presence of non response and measurement errors is of concern while discussing the properties of the proposed estimators. The conditions under which the proposed estimator perform relatively better than the estimators based on recent studies are obtained. Simulation study also carried out in different situations over the data set of natural population and fictitious population to support the theoretical findings. Published on 2021-12-31 00:00:00
Multivariate Modelling of Binary Responses with Normal and
Non–Normal Random Effects
- Abstract: In different fields of study, multivariate binary data is often found, especially when several different qualitative characteristics or attributes are measured in the same unit or from the same person. These bivariate or multivariate responses observed from the same individual or a unit are likely to be correlated. This study aimed to evaluate the influence on the regression estimates of the parameters when binary responses are modeled jointly. The correlation between binary outcomes was captured by incorporating random effects. Normal and bridge distributions were assumed for the random effects. A simulation study was performed to illustrate the impact on the marginal parameter estimates of the joint response model when using the bridge and normal distributions for the random effects. The simulation study revealed that the joint model with either normal or bridge random effects provides a better gain in efficiency in the parameter estimates compared to the individual models which assume responses are independent. Furthermore, the parameter estimates of the joint model are more or less the same under the normal distribution and bridge distribution of the random effects when outcomes are correlated. However, slight differences are noted in the standard errors of the parameter estimates. In addition, when two outcomes are not correlated there is no gain in the fitting joint model over separate univariate models. Finally, these methods were applied to the Bangladesh Demographic and Health Survey 2011 (BDHS 2011) data. Published on 2021-12-31 00:00:00
Estimation of the Parameters of Power Function Distribution based on
Records
- Abstract: This paper estimates the power function distribution parameters and predicts the future record values when samples are available only in the form of upper record values. We considered the maximum likelihood and Bayesian techniques for the estimation. We also construct asymptotic, bootstrap, and HPD confidence intervals for the unknown parameters. Bayes estimators are derived using the squared error loss function, entropy loss function, and Linex loss function using the Lindley approximation and importance sampling procedures. Finally, we conduct a simulation study to compare all the proposed estimation methods and analyse a real data set for illustration purposes. Published on 2021-10-31 00:00:00
New Exponential-Type Estimators of Finite Population Variance Using
Auxiliary Information
- Abstract: In this study, some existing finite population variance estimators for study variable have been modified using linear combination and power improvement techniques. Asymptotic properties (Biases and MSEs) of the suggested estimators are derived up to the terms of first-order approximation using Taylor’s Series expansion. The numerical illustration was also supported by six real-life data sets and simulated data set using R to corroborate the theoretical results. In general, the results reveal that the proposed estimators outperformed the existing estimators considered in the study. Published on 2021-10-31 00:00:00

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