Modelling the Efficiency of TGARCH Model in Nigeria Inflation Rate

In general, volatility is known and referred to as variance and it is a degree of spread of a random variable from its mean value. Two volatility models were considered in this paperwork. Nigeria's inflation rate was modeled by applying the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Threshold GARCH models. Symmetric and asymmetric models captured the most commonly stylized facts about the rate of inflation in Nigeria like leverage effects and irregularities in clustering and were studied. These models are GARCH (1,1) and TGARCH (1,1). This work estimated the comparison of volatility models in term of best fit and forecasting. The result showed that TGARCH (1,1) model outperformed GARCH (1,1) models in term of best fit, because it has the least AIC of 2.590438. We forecasted to see the level of volatility using Theils Inequality Coefficient and the result shows that TGARCH has the highest Theils Inequality Coefficient of 0.065075 which makes the TGARCH model better than the GARCH model in this research. From the initial and modified sample static forecast, it was discovered that the return on inflation is stable and shows that volatility slows towards the end of the month, we can see a downward spiral, which means price reaction to economic crisis led to lower production, lower wages, decreased demand, and still lower prices.

The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data

Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell – Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.

Some Properties and Applications of Topp Leone Kumaraswamy Lomax Distribution

Many Statisticians have developed and proposed new distributions by extending the existing distributions. The distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime distribution called the Topp Leone Kumaraswamy Lomax distribution was introduced by using a family of distributions which has been proposed in the literature. Some mathematical properties of the distribution such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions were presented. The estimation of the parameters by maximum likelihood method was discussed. Three real life data sets representing the failure times of the air conditioning system of an air plane, the remission times (in months) of a random sample of one hundred and twenty-eight (128) bladder cancer patients and Alumina (Al2O3) data were used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in the three datasets considered.

Partitioned and Non-Partitioned Regularized Additive Hazard Models with and Without Spatial Dependence

Spatial effects are often simultaneously investigated with non-linear effects of continuous covariates and the usual linear effect. In this work the performance of models with and without spatial dependence in partitioned (PM) and non-partitioned models (NPM) for four (4) censoring percentages, three(3) levels of Weibull baseline variances (WBV), and sample sizes 100, 500 & 1000 were investigated. Hazard models were adapted to the generalized additive predictors and analyses were carried out via MCMC simulation technique. The performances of the models were again assessed when fitted to the diabetic data set. Results suggest that; partition models outperformed the non-partition ones. Models with spatial dependence perform better than models without spatial dependence in denser event times and when WBVs are low. The partition models perform better with spatial dependence than the Non-partitioned models. For the diabetic data set, it is seen that covariates Age and Blood Sugar level (BSL) violates the proportionality assumptions upon test. Further assessment from the graph of coefficient against time; suggest that Age be put to cut-points while BSL was estimated for models with and without Penalized splines for the sake of comparison, since the graph shows just a slight deviation from proportionality. Hazard rates for the time varying Age; indicate that as the time of study rolls by, the hazard of experiencing the event death from the disease increases steadily between intervals but constant within each time interval. A unit change in hazard rate for BSL indicates a decrease for PM implemented for with and without penalized splines. The model without penalized splines was however, seen to be better with smaller DIC (Deviance Information Criteria) value. Marriage is seen to be significant in the management of the disease in comparison to single patients. In addition patients are advised to visit their physicians on a regular basis to run a routine check to keep their BSL in good range. The study provides a means of moving out of non-linear ruts in survival data analysis. Intervals increase sample sizes (pseudoobservations), which in turn improves the modified Partitioned model when they are with or without spatial dependence.

Monitoring Groundwater Quality using Probability Distribution in Gwale, Kano state, Nigeria

Groundwater is the water present beneath the earth’s surface in soil pore spaces and the fractures of rock formations. Establishing a probability distribution that provides a good fit to groundwater quality has recently become a topic of interest in the fields of hydrology, meteorology among others. In this paper, three groundwater datasets including calcium, magnesium, and chloride are fitted to the normal, lognormal, gamma, Weibull, logistic, and log-logistic distributions to select the best groundwater model. The measures of goodness of fits such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), and log-likelihood are computed to compare the fitted models. The results show that the gamma distribution gives better fits for calcium and magnesium datasets while the lognormal distribution provides a better fit for the chloride dataset than other competing models. This research describes an application of probability distributions and the best-fitted distribution to a practical problem involving groundwater data analysis. By assuming the distribution of data, analysts can utilize the characteristics of the distribution to make predictions on outcomes.

Determinants of Labour Force Participation Rate in Malaysia from Gender Perspective

Labour force participation rate (LFPR) is always a concern in economic view in Malaysia. This research study on how the labour force factors will affect the LFPR according to gender perspective for every state in Malaysia from the year 2011 to 2016. Static Panel Data analysis were used in this study. By using Fixed effect model (FEM), outside labour force, non-married, secondary, and tertiary education level have inverse relationship with male LFPR, while the marital status of labour force has positive relationship with male LFPR. Next, for the effect of determinants and characteristics of labour force on female LFPR, Random effect model (REM) was used. The model shows that unemployed, widowed status, outside labour force, and marital status have an inverse relationship with female LFPR. Meanwhile, non-formal education level, tertiary education level, and age group between 40-64 have positive relationship with female LFPR. In conclusion, it is important to understand the LFPR according to gender in Malaysia because it will shape the comparative advantage and describes the situation of Malaysia’s labour market. This study provides an overview of labour force in Malaysia using an appropriate statistical modelling known as panel data approach.

Comparison of Robust Estimators’ Performance for Detecting Outliers in Multivariate Data

In multivariate data, outliers are difficult to detect especially when the dimension of the data increase. Mahalanobis distance (MD) has been one of the classical methods to detect outliers for multivariate data. However, the classical mean and covariance matrix in MD suffered from masking and swamping effects if the data contain outliers. Due to this problem, many studies used a robust estimator instead of the classical estimator of mean and covariance matrix. In this study, the performance of five robust estimators namely Fast Minimum Covariance Determinant (FMCD), Minimum Vector Variance (MVV), Covariance Matrix Equality (CME), Index Set Equality (ISE), and Test on Covariance (TOC) are investigated and compared. FMCD has been widely used and is known as among the best robust estimator. However, there are certain conditions that FMCD still lacks. MVV, CME, ISE and TOC are innovative of FMCD. These four robust estimators improve the last step of the FMCD algorithm. Hence, the objective of this study is to observe the performance of these five estimator to detect outliers in multivariate data particularly TOC as TOC is the latest robust estimator. Simulation studies are conducted for two outlier scenarios with various conditions. There are three performance measures, which are pout, pmask and pswamp used to measure the performance of the robust estimators. It is found that the TOC gives better performance in pswamp for most conditions. TOC gives better results for pout and pmask for certain conditions.

Best Fitted Distribution For Meteorological Data In Kuala Krai

Modeling meteorological variables is a vital aspect of climate change studies. Awareness of the frequency and magnitude of climate change is a critical concern for mitigating the risks associated with climate change. Probability distribution models are valuable tools for a frequency study of climate variables since it measures how the probability distribution able to fit well in the data series. Monthly meteorological data including average temperature, wind speed, and rainfall were analyzed in order to determine the most suited probability distribution model for Kuala Krai district. The probability distributions that were used in the analysis were Beta, Burr, Gamma, Lognormal, and Weibull distributions. To estimate the parameters for each distribution, the maximum likelihood estimate (MLE) was employed. Goodness-of-fit tests such as the Kolmogorov-Smirnov, and Anderson-Darling tests were conducted to assess the best suited model, and the test's reliability. Results from statistical studies indicate that Burr distributions better characterize the meteorological data of our research. The graph of probability density function, cumulative distribution function as well as Q-Q plot are presented.

A Review on Outliers-Detection Methods for Multivariate Data

Data in practice are often of high dimension and multivariate in nature. Detection of outliers has been one of the problems in multivariate analysis. Detecting outliers in multivariate data is difficult and it is not sufficient by using only graphical inspection. In this paper, a nontechnical and brief outlier detection method for multivariate data which are projection pursuit method, methods based on robust distance and cluster analysis are reviewed. The strengths and weaknesses of each method are briefly discussed.

Comparative Analysis of Classical and Modified Moses Test

Moses test is a nonparametric method to test the equality of two dispersion parameters. The Moses test does not assume equality of location parameters, and this fact gives the test wider applicability. However, this test is inefficient since different people applying the test will obtain different values because of a random process. One sub-division may lead to significant results where another does not. To overcome the problem of uniqueness of the result, this study proposed to modify the random selection of the observation for the subsamples based on the ranking procedure to lead for a unique result for each solution. The original and modified Moses test were tested on the same data set. The finding shows that the result for both tests is similar in terms of decision and conclusion. The analysis revealed that the modified Moses test based on ranking approach has a smaller sum of squared values compared to the original Moses test. Thus, the variability of data for each subsample is decreased as well. Ranking approach can be used as an alternative to replacing the random procedure of selecting observations for subsample to overcome the problem of uniqueness in the test statistic.