Pakistan Journal of Statistics and Operation Research
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A Proposed Method for Finding Initial Solutions to Transportation Problems
No full textThe Transportation Model (TM) in the application of Linear Programming (LP) is very useful in optimal distribution of goods. This paper focuses on finding Initial Basic Feasible Solutions (IBFS) to TMs hence, proposing a Demand-Based Allocation Method (DBAM) to solve the problem. This unprecedented proposal goes in contrast to the Cost-Based Resource Allocations (CBRA) associated with existing methods (including North-west Corner Rule, Least Cost Method and Vogel’s Approximation Method) which make cost cell (i.e. decision variable) selections before choosing demand and supply constraints. The proposed ‘DBAM’ on page 4 is implemented in MATLAB and has the ability to solve large-scale transportation problems to meet industrial needs. A sample of five (5) examples are presented to evaluate efficiency of the method. Initial Basic Feasible Solutions drawn from the study (according to DBAM) represent the optimal with higher accuracy, in comparison to the existing methods. Results from the study qualify the DBAM as one of the best methods to solve industrial transportation problems
The Marshall–Olkin Pareto Type-I Distribution: Properties, Inference under Complete and Censored Samples with Application to Breast Cancer Data
No full textIn this paper, we introduce the Marshall–Olkin Pareto type-I (MOPTI) distribution. Structural properties of the MOPTI distribution including the quantile function, mean residual life, and a new theorem for strength-stress measure are introduced. Five methods of estimation for the MOPTI parameters based on complete samples are presented. Furthermore, we explore the estimation of the MOPTI parameters under type-I and type-II censoring. Two Monte Carlo simulation studies are conducted to evaluate the performance of the estimation methods under complete and censored samples. A real-life data set is used to validate the proposed methods
Marginal and Conditional both Extreme Value Distributions: A Case of Stochastic Regression Model
No full textA mathematical model is a mathematical connection that describes some real-life scenario. To handle real-world problems securely and effectively, simulation modelling is required. In this article, the author investigates the stochastic regression model scenario in which the dependent and independent variables in a linear regression model follow a distribution. We assume that the dependent and independent variables both exhibit Type I Extreme Value Distribution. The estimators are then derived using the Modified Maximum Likelihood (MML) estimation method. In accordance with this, a hypothesis testing technique is developed
The Construction of Unemployment Rate Model Using SAR, Quantile Regression, and SARQR Model
No full textThe Open Unemployment Level (OUL) is the percentage of the unemployed to the total labor force. One of the provinces with the highest OUL score in Indonesia is West Java Province. If an object of observation is affected by spatial effects, namely spatial dependence and spatial diversity, then the regression model used is the Spatial Autoregressive (SAR) model. Quantile regression minimizes absolute weighted residuals that are not symmetrical. It is perfect for use on data distribution that is not normally distributed, dense at the ends of the data distribution, or there are outliers. The Spatial Autoregressive Quantile Regression (SARQR) is a model that combines spatial autoregressive models with quantile regression. This research used the data regarding OUR in West Java in 2020 from the Central Bureau of Statistics. This study compares the estimation results based on SAR and SARQR models to obtain an acceptable model. In this study, it was found that the SARQR model is better than SAR at dealing with the problems of dependency and diversity in spatial data modeling and is not easily affected by the presence of outlier data
A modified weighting system for combined forecasting methods based on the correlation coefficients of the individual forecasting models
No full textHerein, a modified weighting for combined forecasting methods is established. These weights are used to adjust the correlation coefficient between the actual and predicted values from five individual forecasting models based on their correlation coefficient values and ranking. Time-series datasets with three patterns (stationary, trend, or both trend and seasonal) were analyzed by using the five individual forecasting models and three combined forecasting methods: simple-average, Bates-Granger, and the proposed approach. The MAPE and RMSE results indicate that the proposed method outperformed the others, especially when the time-series pattern was stationary and improved the forecasting accuracy of the worst and best individual forecasting models by 35–37% and 7–10%, respectively. Moreover, the proposed method showed improvements in MAPE and RMSE of around 18–20% and 9–11% compared to the simple-average and Bates-Granger methods, respectively. In addition, the combined forecasting methods outperformed the individual forecasting models when analyzing non-stationary data. Remarkably, the performances of the proposed and Bates-Granger methods were almost the same, with improvements in MAPE and RMSE in the range of 1–2% on average. Therefore, the proposed method for creating weights based on the correlation coefficients of the individual forecasting models greatly improves combined forecasting methods
Black hole algorithm as a heuristic approach for rare event classification problem
No full textThe logistic regression is generally preferred when there is no big difference in the occurrence frequencies of two possible results for the considered event. However, for the events occurring rarely such as wars, economic crisis and natural disasters, namely having relatively small occurrence frequency when compared to the general events, the logistic regression gives biased parameter estimations. Therefore, the logistic regression underestimates the occurrence probability of the rare events. In this study, black hole algorithm is proposed and used to obtain unbiased estimation parameters for rare events, instead of using the classical logistic regression approach. In order to estimate the logistic regression parameter for the cases dichotomous event groups are rare, we propose a black hole algorithm (BHA) approach. For the samples with different rareness degrees, we obtain the parameter values and their bias and root mean square errors for BHA and logistic regression, and then compare them. Moreover, we also investigate the classification performance of two methods on a real life data. As a result, we obtained that BHA gives less biased estimates in simulation and real-life data compared to logistic regression
Implementation of Bayesian Simulation for Earthquake Disaster Risk Analysis in Indonesia based on Gutenberg Richter Model and Copula Method
No full textIndonesia is a country prone to earthquakes because it is located in the Pasific ring of fire area. The earthquakes caused a lot of damages and casualties. In this paper, we use Bayesian Simulation on Gutenberg Richter model and Copula method to estimate the risk parameters of earthquake, specifically the probability and the recurrence (return) period of an earthquake occurrence in Indonesia. Those risk parameters are estimated from dependence structure of frequency and magnitude of earthquakes. The dependence structure can be determined by using Gutenberg Richter model and Copula method. The Gutenberg Richter model is a model based on linear regression used to determine dependence structure, while the Copula method is a statistical method used to determine dependence structure that ignores linearity and normality assumptions of data. Bayesian Simulation is a method used to estimate parameters based on simulation. The data used is an annual data of frequency and magnitude (magnitude ≥ 4 Richter Scale) of earthquakes occur in Indonesia for 4 years from Meteorological, Climatological, and Geophysical Agency of Indonesia. There are several steps of analysis to be performed: firstly, we perform regression analysis of frequency and magnitude of the earthquakes to determine Gutenberg Richter Model; secondly, we perform Copula analysis; thirdly, we estimate probability and the recurrence (return) period of an earthquake occurrence using Bayesian Simulation based on the result of step one and two. The result indicates Bayesian Simulation can estimate risk parameters very well
Mean Estimation of a Sensitive Variable under Measurement Errors using Three-Stage RRT Model in Stratified Two-Phase Sampling
No full textIn the present study, the problem of mean estimation of a sensitive variable using three-stage RRT model under measurement errors is addressed. A generalized class of estimators is proposed using a mixture of auxiliary attribute and variable. Some members of the proposed generalized class of estimators are identified and studied. The bias and mean squared error (MSE) expressions for the proposed estimators are correctly derived up to first order Taylor's series of approximation. The proposed estimator's efficiency is investigated theoretically and numerically using real data. From the numerical study, the proposed estimators outperforms existing mean estimators. Furthermore, the efficiencies of the mean estimators’ decreases as the sensitivity level of the survey question increases
The Multimodal Extension of the Balakrishnan Alpha Skew Normal Distribution: Properties and Applications
No full textThis paper introduces a new class of Balakrishnan distribution by extending the multimodal skew-normal distribution proposed by Chakraborty et al. (2015). Statistical properties of the new family of distributions are studied in detail. In particular, explicit expressions of the density and distribution function, moments, skewness, kurtosis and the moments generating function are derived. Furthermore, estimation of the parameters using the maximum likelihood method of the new family of distributions is considered. Finally, the paper ends with an illustration of real-life data sets and then comparing the value of Akaike Information Criterion and Bayesian information criterion of the new distribution with some other known distributions. For the nested models, the Likelihood Ratio Test is carried out
The Marshall-Olkin Pranav distribution: Theory and applications
No full textThe current paper presented new two-parameter life processes distribution, the Marshall-Olkin Pranav (MOEP) distribution. This study combines the Marshall-Olkin method with the Pranav distribution to produce a more accessible and flexible model used to perform data survival techniques. Some of its critical statistical features are presented in this study. For instance, we mentioned its survival , hazard, reversed hazard, and cumulative hazard rate function. Then we discussed its Moment generating functions, The characteristic function, Incomplete moments, R`enyi and Entropies, and stochastic orderings. The research utilized maximization of chance in estimating parameters. These tests are done through simulations to achieve the desired results. After its attainment, real-life data was used to test the new model, which possesses the best goodness of fit