Open Access Original Research Article

Application of Sarima Models in Modelling and Forecasting Monthly Rainfall in Nigeria

Aliyu Sani Aliyu, Abubakar Muhammad Auwal, M. O. Adenomon

Asian Journal of Probability and Statistics, Page 30-43
DOI: 10.9734/ajpas/2021/v13i330310

Application of SARIMA model in modelling and forecasting monthly rainfall in Nigeria was considered in this study. The study utilizes the Nigerian monthly rainfall data between 1980-2015 obtained from World Bank Climate Portal. The Box-Jenkin’s methodology was adopted.  SARIMA (2,0,1) (2,1,1) [12] was the best model among others that fit the Nigerian rainfall data (1980-2015) with maximum p-value from Box-Pierce Residuals Test. The study forecasts Nigeria’s monthly rainfall from 2018 through 2042. It was discovered that the month of April is the period of onset of rainfall in Nigeria and November is the period of retreat. Based on the findings, Nigeria will experience approximately equal amount of rainfall between 2018 to 2021 and will experience a slight increase in rainfall amount in 2022 to about 1137.078 (mm). There will be a decline of rainfall at 2023 to about 1061 (mm). Rainfall values will raise again to about 1142.756 (mm) in 2024 and continue to fluctuate with decrease in variation between 2024 to 2042, then remain steady to 2046 at approximately 1110.0 (mm). Nigerian Government should provide a more mechanized and drier season farming methods to ease the outage of rainfall in future that may be caused due to natural (or unpredictable) variation.

Open Access Original Research Article

A New Algorithm for Approximate Maximum Likelihood Estimation in Sub-fractional Chan-Karolyi-Longstaff-Sanders Model

Jaya P. N. Bishwal

Asian Journal of Probability and Statistics, Page 62-88
DOI: 10.9734/ajpas/2021/v13i330311

The paper introduces several approximate maximum likelihood estimators of the parameters of the sub-fractional Chan-Karolyi-Longstaff-Sanders (CKLS) interest rate model and obtains their rates of convergence. A new algorithm inspired by Newton-Cotes formula is presented to improve the accuracy of estimation. The estimators are useful for simulation of interest rates. The proposed new algorithm could be useful for other stochastic computation. It also proposes a generalization of the CKLS interest rate model with sub-fractional Brownian motion drivers which preserves medium range memory.

Open Access Review Article

A Study on Various Transformation Method of Weibull Distribution: A Review

Seema Chettri, Bhanita Das

Asian Journal of Probability and Statistics, Page 1-12
DOI: 10.9734/ajpas/2021/v13i330307

In this article a brief summary of some recent developments of Weibull lifetime models has been presented for a quick overview. Various extensions of the Weibull models and the properties of the extended Weibull distribution have been discussed. A brief discussion about the characteristics and shape behaviour has been presented in the tabular form. Finally, some future research topics have been given.

Open Access Review Article

Difference-Cum-Ratio Estimators for Estimating Finite Population Coefficient of Variation in Simple Random Sampling

A. Audu, M. A. Yunusa, O. O. Ishaq, M. K. Lawal, A. Rashida, A. H. Muhammad, A. B. Bello, M. U. Hairullahi, J. O. Muili

Asian Journal of Probability and Statistics, Page 13-29
DOI: 10.9734/ajpas/2021/v13i330308

In this paper, three difference-cum-ratio estimators for estimating finite population coefficient of variation of the study variable using known population mean, population variance and population coefficient of variation of auxiliary variable were suggested. The biases and mean square errors (MSEs) of the proposed estimators were obtained. The relative performance of the proposed estimators with respect to that of some existing estimators were assessed using two populations’ information. The results showed that the proposed estimators were more efficient than the usual unbiased, ratio type, exponential ratio-type, difference-type and other existing estimators considered in the study.

Open Access Review Article

Generalized Rank Mapped Transmuted Distributions with Properties and Application: A Review

. Imliyangba, Bhanita Das, Seema Chettri

Asian Journal of Probability and Statistics, Page 44-61
DOI: 10.9734/ajpas/2021/v13i330309

Generalizing probability distributions is a very common practice in the theory of statistics. Researchers have proposed several generalized classes of distributions which are very flexible and convenient to study various statistical properties of the distribution and its ability to fit the real-life data. Several methods are available in the literature to generalize new family of distributions. The Quadratic Rank Transmutation Map (QRTM) is a tool for the construction of new families of non-Gaussian distributions and to modulate a given base distribution for modifying the moments like the skewness and kurtosis with the ability to explore its tail properties and improve the adequacy of the distribution. Recently, a new family of transmutation map, defined as Cubic Rank Transmutation (CRT) has been used by several authors to develop new distributions with application to real-life data. In this article, we have done a review work on the existing generalized rank mapped transmuted probability distributions, available in the literature with various statistical properties such as the reliability, hazard rate and cumulative hazard functions, moments, mean, variance, moment-generating function, order statistics, generalized entropy and quantile function along with its applications. Some future works have also been discussed for generalized rank mapped transmuted distributions.