Open Access Original Research Article

The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application

Mustapha Muhammad, Isyaku Muhammad, Aisha Muhammad Yaya

Asian Journal of Probability and Statistics, Page 1-17
DOI: 10.9734/ajpas/2018/v1i324532

In this paper, a new lifetime model called Kumaraswamy exponentiated U-quadratic (KwEUq) distribution is proposed. Several mathematical and statistical properties are derived and studied such as the explicit form of the quantile function, moments, moment generating function, order statistics, probability weighted moments, Shannon entropy and Renyi entropy. We also found that the usual maximum likelihood estimates (MLEs) fail to hold for the KwEUq distribution. Two alternative methods are suggested for the parameter estimation of the KwEUq, the alternative maximum likelihood estimation (AMLE) and modified maximum likelihood estimation (MMLE). Simulation studies were conducted to assess the finite sample behavior of the AMLEs and MMLEs. Finally, we provide application of the KwEUq for illustration purposes.

Open Access Original Research Article

Generalized Euclidean Least Square Approximation

A. S. Oke, S. M. Akintewe, A. G. Akinbande

Asian Journal of Probability and Statistics, Page 1-10
DOI: 10.9734/ajpas/2018/v1i324535

A Generalised Euclidean Least Square Approximation (ELS) is derived in this paper. The Generalised Euclidean Least Square Approximation is derived by generalizing the interpolation of n arbitrary data set to approximate functions. Existence and uniqueness of the ELS schemes are shown by establishing the invertibility of the coefficient matrix using condensation method to reduce the matrix. The method is illustrated for exponential function and the results are compared to the classical Maclaurin’s series.

Open Access Original Research Article

Analysis of Rainfall Pattern in the Western Region of Ghana

Frank B. K. Twenefour, Michael Techie Quaicoe, Emmanuel M. Baah

Asian Journal of Probability and Statistics, Page 1-12
DOI: 10.9734/ajpas/2018/v1i324538

The primary aim for this paper is to examine the pattern of rainfall in the western region of Ghana. Data was obtained from the Ghana Meteorological Agency. The sample include January to September pattern of the amount of rainfall, for the years 2006 to 2016. That is nominal daily rainfall recorded (1485) aggregated into monthly rainfall value (99 data point). The analysis includes fitting an auto regression moving average model (ARMA) model for the data. The series was found to be non-stationary which resulted from the presence of a unit root in it. The series became stationary after eliminating the unit root by finding the first difference in the amount of rainfall. The time series component found in the model were a trend and random variation. ARMA (1, 1) which has all parameters significant was fitted for the data and found to be the most  suitable model for the conditional mean. A Ljung Box test statistic of 47.207 with a normalised BIC of 6.420 and a Root Mean Square error of 24.16 supported by a probability value of 0.001 show that the fitted model is appropriate for the data. An = 0.532 indicates that about 53% of the variations seen in the pattern of rainfall recorded for the period is being explained by the fitted model. The 18-month forecast for the mean actual rainfall and mean returns could show that the fitted model is appropriate for the data and an increasing trend of rainfall for the forecasted period.

 

Open Access Original Research Article

Refinements of Gaussian Tail Inequality

N. A. Rather, T. A. Rather

Asian Journal of Probability and Statistics, Page 1-8
DOI: 10.9734/ajpas/2018/v1i324541

In this paper, we first prove a theorem which gives considerably better bound for 0 ≤ t ≤ 1/2 than Gaussian tail inequality (or tail bound for normal density) and thus is a refinement of Gaussian tail inequality in this case. Next we present an interesting result which provides a refinement of Gaussian tail inequality for t > √ 3. Besides, we also prove an improvement of Gaussian tail inequality for 0 < t ≤ 1/2. Finally, we present a more general result which includes a variety of interesting results as special cases.

Open Access Original Research Article

The Transmuted Odd Lindley-G Family of Distributions

Hesham Reyad, Farrukh Jamal, Soha Othman, G. G. Hamedani

Asian Journal of Probability and Statistics, Page 1-25
DOI: 10.9734/ajpas/2018/v1i324544

We propose a new generator of univariate continuous distributions with two extra parameters called the transmuted odd-Lindley generator which extends the odd Lindely-G family introduced by Gomes-Silva et al. [1]. Some mathematical properties of the new generator such as, the ordinary and incomplete moments, generating function, stress strength model, Rényi entropy, probability weighted moments and order statistics are investigated. Certain characterisations of the proposed family are estimated. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. The potentiality of the new family is illustrated by means of five applications to real data sets.