Unilag Journal of Mathematics and Applications

EXISTENCE OF WEAK SOLUTIONS FOR THE INCOMPRESSIBLE NONLINEAR PARABOLIC SYSTEM WITH DAMPING

2023-04-29T07:56:02+00:00

This work concerns the existence of the weak solutions associated with the incompressible
parabolic system with damping. The solution is shown to exist with data in Lesbegue space, L².

CAPTURING EXCESS ZEROS IN MODELING AUTO-INSURANCE CLAIMS IN AN INDIGENOUS INSURANCE FIRM USING ZERO INFLATED MODELS AND HURDLE MODELS

2023-04-29T07:56:02+00:00

Count data occur naturally in a number of disciplines ranging from economics and social sciences to finance as well as medical sciences. Most count data are plagued with over-dispersion and excess zeros making it difficult to model them with vanilla linear models. Different models have been proposed to capture this peculiarity in count data viz.: A number of classical regression models such as the generalized Poisson and negative binomial have been used to model dispersed count data. Hurdle and zero-inflated models are also said to be able to capture over-dispersion and excess zeros in count data.

In this paper, we compare the performance of Poisson and Negative Binomial hurdle models, zero-inflated Poisson and Negative Binomial models, classical Poisson and Negative Binomial regression models as well as the zero-inflated compound Poisson generalized linear models to modelling frequency of auto insurance claims in a typical emerging market.

The model parameters are estimated using the method of maximum likelihood. The models performances are compared based based on some model selection criteria, including: Akaike and Bayesian information Criteria (AIC and BIC), and Gini index. The zero-inflated compound Poisson generalized linear models performed better than the other models considered.

PARAMETRIC MODELLING USING BAYESIAN APPROACH

2023-04-29T07:56:02+00:00

In this paper, we focus on the applicability of a Bayesian analysis to survival time of breast cancer data by assuming that the survival times
follow a Weibull distribution. This study determines a method of estimating the model parameters in survival analysis. The proportional hazard model is
used to relate the hazard function to the covariate values for an individual. The scale parameter of a Weibull distribution is used to incorporate the covariates of the individual and the linear predictor is expressed as a logarithmic link function of the hazard multiplier. The Bayesian approach to survival analysis is used via the Just another Gibbs sampler (RJAGS) program in R language and R functions was used to calculate the prognostic index as a linear predictor on an index from 0 to 100 which is used for predicting the outcome of the patients on the basis of the clinical information. The posterior summaries of interest which were derived from the posterior distribution are provided. The results from the posterior distribution obtained from this study can be used in the calculation of the risk value of the breast cancer patient. Thus, the risk value helps the researcher to have an assess to the patients exposure to breast cancer. The Parametric model was seen to be a very attractive option of modelling and the ease of interpretation of parameters is of benefit especially for clinicians.

WEIBULL-LOGISTIC WITH EXPONENTIAL QUANTILE FUNCTION DISTRIBUTION

2023-04-29T07:56:02+00:00

The T-R{Y} is a T-X method of using a quantile function to generate probability distributions. It is a generalization of the T-X, Beta-X and many other families. This paper developed a 4-parameter Weibull-Logistic distribution using the T-R{Y} framework. This was achieved by combining the flexibility of the Weibull distribution with the two-parameter logistic distribution that has a location parameter, using the standard quantile function of the exponential distribution. Properties of the resulting distribution are extensively investigated, viz; rth non-central moments, quantiles, mode, survival function and hazard function. Plots of its density and cumulative distribution functions were presented to show its various shapes such as skewness or normal-type for some parameters’ values. The Logistic, Weibull, Weibull-logistic and skew logistic distributions are sub-models of the 4-parameter Weibull-Logistic distribution. The distribution is also found to relate with the Weibull distribution through its quantile function, a general feature of the T-R{Y} family. The maximum likelihood method was used to estimate the parameters of the distribution. Simulation study was carried out to show the consistency of its maximum likelihood parameters estimated, and it showed that the shape of the distribution approaches symmetry as the sample size increases. The applicability of the distribution was demonstrated using real life dataset and the likelihood ratio test showed that the location parameter is significant. The proposed distribution would be very useful in areas where Weibull and Logistic distributions are not good fit. The new generator can also be used to generate many other distributions in this family.

COMPARATIVE STUDY OF BAYESIAN AND ORDINARY LEAST SQUARES APPROACHES

2023-04-29T07:56:02+00:00

Frequentist (Classical) and Bayesian are two major approaches to data analysis in statistics, however, the difference is how both see a parameter. Frequentists see a parameter as constant value while the Bayesians see it a random variable. Research work recently has witnessed increase in the application of Bayesian methods to statistical problems and in other fields. For linear regression modelling, frequentists use more often the Ordinary Least Squares (OLS) method despite violation of some assumptions. Bayesian approach can be used when assumptions in linear regression model using OLS are not met. Using two different data sets, an empirical study was performed using both OLS and Bayesian approaches to linear regression modelling. The analysis showed that the resulting linear regression model using OLS does not meet all required assumptions for a good model. The Bayesian approach as an alternative to regression modelling was further established based on results using several criteria such as RMSE, MAPE and MAD. The results showed that linear regression modelling using Bayesian approach is better than Frequentist method using OLS regression modelling.

POSITIVE SOLUTIONS FOR A NONLINEAR FRACTIONAL BOUNDARY VALUE PROBLEM

2023-04-29T07:56:02+00:00

In this paper, we establish the existence of positive solutions to
a nonlinear fractional differential equation with integral boundary conditions.
Our approach is based on the linear operator theory and the application of
Krasnosel’skii fixed-point theorem in a cone. We present two examples to
illustrate the practicability of our main results.