##### Scaled Prediction Variances of Equiradial Design under Changing Design Sizes, Axial Distances and Center Runs

Bartholomew, Desmond Chekwube, Obite, Chukwudi Paul, Ismaila-Cosmos Joan

Asian Journal of Probability and Statistics, Page 1-13
DOI: 10.9734/ajpas/2021/v11i130256

The aim of every design choice is to minimize the prediction error, especially at every location of the design space, thus, it is important to measure the error at all locations in the design space ranging from the design center (origin) to the perimeter (distance from the origin). The measure of the errors varies from one design type to another and considerably the distance from the design center. Since this measure is affected by design sizes, it is ideal to scale the variance for the purpose of model comparison. Therefore, we have employed the Scaled Prediction Variance and D – optimality criterion to check the behavior of equiradial designs and compare them under varying axial distances, design sizes and center points. The following similarities were observed: (i) increasing the design radius (axial distance) of an equiradial design changes the maximum determinant of the information matrix by five percent of the new axial distance (5% of 1.414 = 0.07) see Table 3. (ii) increasing the nc center runs  pushes the maximum  SPV(x) to the furthest distance from the design center (0  0) (iii) changing the design radius changes the location in the design region with maximum SPV(x) by a multiple of the change and (iv) changing the design radius also does not change the maximum  SPV(x) at different radial points and center runs . Based on the findings of this research, we therefore recommend consideration of equiradial designs with only two center runs in order to maximize the determinant of the information matrix and minimize the scaled prediction variances.

##### Kumaraswamy Distribution Based on Alpha Power Transformation Methods

H. E. Hozaien, G. R. AL Dayian, A. A. EL-Helbawy

Asian Journal of Probability and Statistics, Page 14-29
DOI: 10.9734/ajpas/2021/v11i130257

In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.

##### Second Order Rotatable Designs of Second Type Using Central Composite Designs

P. Chiranjeevi, K. John Benhur, B. Re. Victor Babu

Asian Journal of Probability and Statistics, Page 30-41
DOI: 10.9734/ajpas/2021/v11i130258

Kim [1] introduced rotatable central composite designs of second type with two replications of axial points for 2≤v≤8 (v: number of factors). In this paper we have extended the work of Kim [1] for second order rotatable designs of second type using central composite designs for 9≤v≤17.

##### Parameter Estimation of Length Biased Weighted Frechet Distribution via Bayesian Approach

Arun Kumar Rao, Himanshu Pandey

Asian Journal of Probability and Statistics, Page 42-51
DOI: 10.9734/ajpas/2021/v11i130259

In this paper, length-biased weighted Frechet distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

##### Nwikpe Probability Distribution: Statistical Properties and Goodness of Fit

Barinaadaa John Nwikpe, Isaac, Didi Essi, Amos Emeka

Asian Journal of Probability and Statistics, Page 52-61
DOI: 10.9734/ajpas/2021/v11i130260

In this paper, we introduce a new continuous probability distribution developed from two classical distributions namely, gamma and exponential distributions. The new distribution is called the Nwikpe distribution. Some statistical properties of the new distribution were derived. The shapes of its probability density function have been established for different values of the parameters.  The moment generating function, the first four raw moments, the second moment about the mean, Renyi’s entropy and the distribution of order statistics were derived. The parameter of the new distribution was estimated using maximum likelihood method. The shape of the hazard function of the new distribution is increasing. The flexibility of the distribution was shown using some real life data sets, the goodness of fit shows that the new distribution gives a better fit to the data sets used in this study than the one parameter exponential, Shanker, Lindley, Akash, Sujatha and Amarendra distributions.