Sri Lankan Journal of Applied Statistics Latest Articleshttps://sljastats.sljol.info/articles/Latest articles published by Sri Lankan Journal of Applied Statisticsen-usFri, 24 Jan 2020 14:37:34 -0000On The Bayesian Analysis of Censored Mixture of Two Topp-Leone Distributionhttps://sljastats.sljol.info/article/10.4038/sljastats.v19i1.7993This paper develops a Bayesian analysis in the context of non-informative priors for the shape parameter of the mixture of Topp-Leone using the censored data. A population of certain objects is assumed to be composed of two subgroups mixed together in an unknown proportion. The random observation taken from this population is supposed to be characterized by one of the two distinct unknown members of a Topp-Leone distribution. We model the heterogeneous population using two components mixture of the Topp-Leone distribution. A comprehensive simulation scheme has been carried out to highlight the properties and behavior of the estimates in terms of sample size, corresponding risks and the mixing weights. A censored mixture data is simulated by probabilistic mixing for the computational purpose. The Bayes estimators of the said parameters have been derived under the assumption of non-informative priors using different loss functions. Posterior risks of the Bayes estimators are compared to explore the effect of prior information and loss functions. Bayes estimators assuming the uniform prior have been observed performing better. Published on 2019-12-31 03:37:26https://sljastats.sljol.info/article/10.4038/sljastats.v19i1.7993Joint Multilevel Model for Analyzing Length of Stay through Competing Endpoints in Dengue Epidemiologyhttps://sljastats.sljol.info/article/10.4038/sljastats.v19i1.7997Dengue is a common mosquito-borne tropical disease caused by a virus. It is a life threatening disease since it sometimes leads to death within a short period of time. Multilevel modeling is a form of statistical modeling when data is at different levels. Due to dengue seriousness and risk being more similar for patients within districts than between districts, there is correlation between patients within districts. Thus district has to be taken as a cluster variable. A frequently encountered response in epidemiological studies is the length of Stay (LOS) of a patient, which measures the time until the event of interest occurs. Complexity arises with the different states/destinations of the time event and competing risk modelling is a more appropriate method for handling such states. The association of platelet count and length of stay of a dengue patient leads to the joint modelling approach for analyzing the dengue patients. Formulation criteria for the joint model with clustered data is to link these models through two sub models that is by using the multilevel multinomial logistic model for the LOS of dengue patients with different destinations and multilevel continuous model for the log platelet count. The linkage between two responses was derived by sharing a common random effect. Factors that have an effect on different destinations of LOS are, time indicators, year, age, classification, rainfall, temperature and humidity, while age, sex, classification, year place treated, rainfall, temp and humidity are associated factors for the log platelet count of dengue patients. Moreover, supremacy of joint modelling was proved by the AIC and BIC values over two separate univariate models. Published on 2019-12-31 03:37:16https://sljastats.sljol.info/article/10.4038/sljastats.v19i1.7997On Some Properties and Applications of Intervened Gegenbauer Distributionhttps://sljastats.sljol.info/article/10.4038/sljastats.v19i1.7926In this paper, an intervened version of the Gegenbauer distribution is considered and investigated some of its statistical properties. The parameters of the distribution are estimated by the method of maximum likelihood and illustrated using real life data sets. The likelihood ratio test procedure is applied for examining the significance of the intervention parameters and a simulation study is carried out for assessing the performances of the maximum likelihood estimators. Published on 2019-12-31 03:37:06https://sljastats.sljol.info/article/10.4038/sljastats.v19i1.7926Recovering Fisher-Information from the MGF Alone without Requiring Explicit PMF or PDF from a One-Parameter Exponential Familyhttps://sljastats.sljol.info/article/10.4038/sljastats.v19i1.7984It is well-known that a finite <em>moment generating function</em> (m.g.f.) corresponds to a unique probability distribution. So, an important question arises: Is it possible to obtain an expression of Fisher-information, <em>I<sub>X</sub>(Ɵ)</em>; using the m.g.f. alone, that is without requiring explicitly a <em>probability mass function</em> (p.m.f.) or <em>probability density function</em> (p.d.f.), given that the p.m.f. or p.d.f came from a one-parameter exponential family? We revisit the core of statistical inference by developing a clear link (Theorem 1.1) between the m.g.f. and <em>I<sub>X</sub>(Ɵ)</em>. Illustrations are included. Published on 2019-12-31 03:36:54https://sljastats.sljol.info/article/10.4038/sljastats.v19i1.7984Fractional transportation problem with non-linear discount costhttps://sljastats.sljol.info/article/10.4038/sljastats.v18i3.7935The generalization of linear programming is a fractional programming where the objective function is a proportion of two linear functions. Likewise, in fractional transportation problem the aim is to optimize or improve the ratio of two cost functions or damage functions or demand functions. Since the ratio of two functions is considered, the fractional programming models become more appropriate for dealing with real life problems. The fractional transportation problem (FTP) plays a very important role in supply management for reducing cost and amending service. In real life, the parameters in the models are rarely known exactly and have to be evaluated. This paper investigates the fractional transportation problem (FTP) with some discount cost that avails during the shipment time. The transportation problem, which is one of integer programming problems, deals with distributing any commodity from any group of 'sources' to any group of destinations or 'sinks' in the most effective way with a given 'supply' and 'demand' constraints. The volume of goods to be transported from one place to another incurs some discount cost that could effectively reduce the shipment cost which is directly related to the profit associated with the shipment. This paper is aimed at studying the optimal solution for the problem has been achieved by using Karush-Kuhn-Tucker (KKT) optimality algorithm. Finally, a numerical example is illustrated to support the algorithm. Published on 2017-12-31 00:00:00https://sljastats.sljol.info/article/10.4038/sljastats.v18i3.7935SAI method for solving job shop sequencing problem under certain and uncertain environmenthttps://sljastats.sljol.info/article/10.4038/sljastats.v18i3.7911In this investigation, we use SAI method (Gupta et al. 2016), for solving sequencing problem when processing time of the machine is certain or uncertain in nature. The procedure adopted for solving the sequencing problems is easiest and involves the minimum numbers of iterations to obtain the sequence of jobs. The uncertainty in data is represented by triangular or trapezoidal fuzzy numbers. Yager’s ranking function approach is used to convert these fuzzy numbers into a crisp at a prescribed value of α. Stepwise SAI method is then used to obtain optimal job sequence for the problem. Further, the result obtained by SAI method is compared with Johnson’s Method. Numerical examples are given to demonstrate the effectiveness of the proposed approach. Published on 2017-12-31 00:00:00https://sljastats.sljol.info/article/10.4038/sljastats.v18i3.7911The transmuted geometric-inverse weibull distribution: properties, characterizations and applicationhttps://sljastats.sljol.info/article/10.4038/sljastats.v18i3.7959In this paper, a four parameters flexible life time distribution called the transmuted geometric-inverse Weibull (TG-IW) distribution is obtained from mixture of inverse Weibull distribution, geometric distribution and transmuted distribution. Some structural and mathematical properties including descriptive measures on the basis of quantiles, moments, factorial moments, incomplete moments, inequality measures, residual life functions and some other properties are theoretically taken up. The TG-IW distribution is characterized via different techniques. The estimates of parameters for the TG-IW distribution are being obtained from maximum likelihood method. The significance and flexibility of the TG-IW distribution is tested through different measures by application to physical data set. Published on 2017-12-31 00:00:00https://sljastats.sljol.info/article/10.4038/sljastats.v18i3.7959An appraisal on some methods for estimating the 2-parameter weibull distribution with application to wind speeds samplehttps://sljastats.sljol.info/article/10.4038/sljastats.v18i3.8001Six<em> </em>methods for estimating the Weibull shape and scale parameters are considered and compared in this paper. These methods are: the least squares method, weighted least squares method, method of moments, energy pattern factor method, method of L-moments and the maximum likelihood method. A simulation study as well as application to a real data set (wind speeds sample) was used to test the performance of different methods using the smallest mean square error criterion. Results from the simulation study indicated that the maximum likelihood method is the most efficient method when dealing with large sample sizes, while the weighted least squares method, method of moments and the method of L-moments were quite efficient for small and moderate sample sizes. The maximum likelihood method produced the best method when all six methods were applied to a wind speeds sample by possessing the smallest mean square error. A very useful result obtained from the study is that the weighted least squares method which performed considerably well in estimating the Weibull parameters. This is a rare incidence in many studies. Published on 2017-12-31 00:00:00https://sljastats.sljol.info/article/10.4038/sljastats.v18i3.8001Developing a surrogate endpoint for AIDS clinical trialshttps://sljastats.sljol.info/article/10.4038/sljastats.v18i2.7955When it comes to the process of developing new treatments, the choice of an endpoint is very crucial because this endpoint will be used to assess the effects of the treatments. However the most sensitive and clinically relevant endpoint which is called the ‘true endpoint’ is difficult to use in a clinical trial because the measurement of the true endpoint can be costly and difficult to measure. In such cases the most feasible solution is to replace the true endpoint by another endpoint termed ‘surrogate endpoint’ which can be measured earlier and frequently.CD4 and viral loads are used in majority of AIDS clinical trials as surrogate endpoints, however, no surrogate endpoint has yet been shown to be suitable in forecasting the effectiveness of anti-HIV treatments. As a solution, the current study is intended on developing a surrogate endpoint for AIDS based on a combination of variables. This study consists of 16 variables measured in 1151 HIV infected patients. From descriptive statistics, variables CD4 cell count and Karnofsky score were identified as potential candidates for surrogate. However a model with a combination of variables named score consisting of CD4, Karnofsky score and age yielded positive results in the log rank test and conventional statistics. Validation of the scoring model using Prentice’s criteria fulfilled all four criteria of Prentice and the model was also successful in identifying the difference between the two treatments. When a comparison was made between CD4 cell count and the combined variable model as possible surrogate endpoints for AIDS, the combined variable model proved to be successful in almost every aspect. Also these results surpassed the results in past similar studies. Published on 2017-12-26 00:00:00https://sljastats.sljol.info/article/10.4038/sljastats.v18i2.7955Distribution of body mass index of Indian women: a study based on NFHS-2 and NFHS-3https://sljastats.sljol.info/article/10.4038/sljastats.v18i2.7958World Health Organization recommended Body Mass Index (BMI) as a measure of nutritional status of adults. This study investigates the distribution of BMI and its changes among Indian women in the age-group 15-49 years based on sampled data of 83,646 and 111,983 women from the National Family Health Survey-2 (NFHS-2) and NFHS-3 respectively. Background characteristics (BC) specific distributional changes in BMI are demonstrated by (i) fitting an appropriate probability distributions (ii) partial sum based on percentiles of distribution and (iii) test of equality of percentiles of distribution of BMI from NFHS-2 and NFHS-3. Relative measures R1 and R2 are defined to demonstrate burden of underweight and obesity. Changes in the prevalence of underweight, obesity and annual gain in mean BMI for synthetic cohort by age-groups are presented. Rapid increments are observed in mean and higher percentiles of BMI among married women, women in the higher age-groups, and women from south zone of India. High prevalence of underweight is observed among rural women (40.6%) and women from low standard of living (49.7%). Double burden of underweight and obesity is reported among older, rich and highly educated women and women from Christian and Sikh religions. Tests of equality of percentiles of BMI are rejected ( Published on 2017-12-26 00:00:00https://sljastats.sljol.info/article/10.4038/sljastats.v18i2.7958