Asian Journal of Probability and Statistics

Generally in our day to day life we come across the real life situations when right decision making becomes difficult. In different fields like economics, social science, medical science, environment, where such complicacy arises and involves uncertainties. The conventional mathematical methods are unsuitable to solve such problems. To solve this problem, we are to find the various parameters related to the problem to use them to get the accurate result. So fuzzy soft set theory is the best mathematical tool for solving such problems using different techniques. In this research paper, we have taken a multi-criteria real life problem to select a suitable city which suits the best conditions as per the given parameters. For getting the solution, we used average fs-aggregation algorithm for using multi-criteria parameters.

High quality solar radiation data is required for the appropriate monitoring and analysis of the Earth’s climate system as well as efficient planning and operation of solar energy systems. However, well maintained radiation measurements are rare in many regions of the world. Therefore, satellite-derived radiation estimates are an alternative to these scarce solar radiation measurements from the weather stations. Satellite estimates of solar radiation have an advantage over solar radiation measurements from weather stations because of their high spatial and temporal resolutions. These satellite radiation estimates at approximately 5-6 Km resolution derived from geostationary Meteosat satellites are available through the EUMETSAT Satellite Application Facilities (SAFs). CM-SAF (SAF on Climate Monitoring) provides consistent dataset of hourly, daily and monthly solar radiation from 1983 to 2013. In this study, we examined the potential of using satellite estimates of solar radiation to fill in the data gaps in records from the weather stations as well as the areas where radiation data is not available. The analysis carried out showed that the satellite data had fewer missing values than the ground data, and that they are both similar in distribution. The average correlation between the two data sets was found to be 0.71 for both monthly and daily analysis. However, the month of September showed a very low correlation of 0.21. Mean percentage error, mean bias error and mean absolute deviation were found to be 2.46, 18.84, 50.32 and 3.08, 559.87, 1135.93 for daily and monthly analysis, respectively.

The solar radiation distribution in Dodoma was found to follow Weibull distribution throughout the year.

Linear regression is the measure of relationship between two or more variables known as dependent and independent variables. Classical least squares method for estimating regression models consist of minimising the sum of the squared residuals. Among the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) between the independent variables. Violation of this assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This study, therefore, determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity in the explanatory variables. Simulation techniques were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity. Their performances were compared at different sample sizes. Finite properties of estimators’ criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity and sample size. The results showed that, LAD was the best at different levels of multicollinearity and was recommended as alternative to OLS under this condition. The performances of the two estimators decreased when the levels of multicollinearity was increased.

In this paper, the estimators of variance components are derived of two-way nested random model when the problem of missing information exists using combination between Modified Minimum Variance Quadratic Unbiased Estimation (MMIVQUE) and Modified Minimum Variance Quadratic Unbiased Estimation (MMIVQUE (0)) methods that is called MMIV(MIV(0)) method.

Probability distributions and their generalisations have contributed greatly in the modeling and analysis of random variables. However, due to the increased introduction of new distributions there has been a major problem with choosing and applying the right distribution for a given set of data. In most cases, it is discovered that the data set in question fits two or more probability distributions and hence one must be chosen among others. The Lomax-Weibull and Lomax-Log-Logistic distributions introduced in an earlier study using a Lomax-based generator were found to be positively skewed and may be victims of this situation especially when modelling positively skewed datasets. In this article, we apply the two distributions to some selected datasets to compare their performance and provide useful insight on how to select the most fit among them when dealing with a real-life situation. We used the log-likelihood value, AIC, CAIC, BIC, HQIC, Cramér-Von Mises (W*) and Anderson Darling (A*) statistics as performance evaluation tools for selecting between the two distributions.