##### A Construction Technique for Group Divisible (v-1,k,0,1) Partially Balanced Incomplete Block Designs (PBIBDs)

Oluwaseun A. Otekunrin, Kehinde O. Alawode

Asian Journal of Probability and Statistics, Page 23-30
DOI: 10.9734/ajpas/2021/v14i130319

Group Divisible PBIBDs are important combinatorial structures with diverse applications. In this paper, we provided a construction technique for Group Divisible (v-1,k,0,1) PBIBDs. This was achieved by using techniques described in literature to construct Nim addition tables of order 2n, 2≤n≤5 and (k2,b,r,k,1)Resolvable BIBDs respectively. A “block cutting” procedure was thereafter used to generate corresponding Group Divisible (v-1,k,0,1) PBIBDs from the (k2,b,r,k,1)Resolvable BIBDs. These procedures were streamlined and implemented in MATLAB. The generated designs are regular with parameters(15,15,4,4,5,3,0,1);(63,63,8,8,9,7,0,1);(255,255,16,16,17,15,0,1) and (1023,1023,32,32,33,31,0,1). The MATLAB codes written are useful for generating the blocks of the designs which can be easily adapted and utilized in other relevant studies.   Also, we have been able to establish a link between the game of Nim and Group Divisible (v-1,k,0,1) PBIBDs.

##### Samade Probability Distribution: Its Properties and Application to Real Lifetime Data

Asian Journal of Probability and Statistics, Page 1-11
DOI: 10.9734/ajpas/2021/v14i130317

A new two-parameter lifetime distribution has been proposed in this study. The distribution is called Samade distribution. The model is motivated by the wide use of the lifetime models derived from the mixture of gamma and exponential distributions. Its mathematical properties which include the first four moments, variance as well as coefficient of variation, reliability function, hazard function, survival function, Renyi entropy measure and distribution of order statistics have been successfully derived. The maximum likelihood estimation of its parameters and application to real life data have been discussed. Application of this model to three real datasets shown that the proposed model yields a satisfactorily better fit than other existing lifetime distributions. The comparism of goodness-of-fits were established using -2Loglikelihood, AIC and BIC.

##### Tornumonkpe Distribution: Statistical Properties and Goodness of Fit

Asian Journal of Probability and Statistics, Page 12-22
DOI: 10.9734/ajpas/2021/v14i130318

A new sole parameter probability distribution named the Tornumonkpe distribution has been derived in this paper. The new model is a blend of gamma (2,  and gamma(3  distributions. The shape of its density for different values of the parameter has been shown.  The mathematical expression for the moment generating function, the first three raw moments, the second and third moments about the mean, the distribution of order statistics, coefficient of variation and coefficient of skewness has been given. The parameter of the new distribution was estimated using the method of maximum likelihood. The goodness of fit of the Tornumonkpe distribution was established by fitting the distribution to three real life data sets. Using -2lnL, Bayesian Information Criterion (BIC), and Akaike Information Criterion(AIC) as criterial for selecting the best fitting model, it was revealed that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used.

##### SACF of the Errors of Stationary Time Series Models in the Presence of a Large Additive Outlier

R. Suresh

Asian Journal of Probability and Statistics, Page 31-40
DOI: 10.9734/ajpas/2021/v14i130320

In this paper, the limiting behaviour of the Sample Autocorrelation Function(SACF) of the errors {et} of First-Order Autoregressive (AR(1)), First-Order Moving Average (MA(1)) and First Order Autoregressive First-Order Moving Average (ARMA(1,1)) stationary time series models in the presence of a large Additive Outlier(AO) is discussed. It is found that the errors which are supposed to be uncorrelated due to either white noise process or normally distributed process are not so in the presence of a large additive outlier. The SACF of the errors follows a particular pattern based on the time series model. In the case of AR(1) model, at lag 1, the contaminated errors {et} are correlated, whereas at higher lags, they are uncorrelated. But in the MA(1) and ARMA(1,1) models, the contaminated errors {et} are correlated at all the lags. Furthermore it is observed that the intensity of correlations depends on the parameters of the respective models.