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In the logistic regression model, the variance of the maximum likelihood estimator is inflated and unstable when the multicollinearity exists in the data. There are several methods available in literature to overcome this problem. We propose a new stochastic restricted biased estimator. We study the statistical properties of the proposed estimator and compare its performance with some existing estimators in the sense of scalar mean squared criterion. An example and a simulation study are provided to illustrate the performance of the proposed estimator. [ABSTRACT FROM AUTHOR]

For modelling the directional spectra of ocean waves, Cartwright introduced a power-of-cosine circular distribution, (cf. Cartwright, D. E. (1963), “The use of directional spectra in studying the output of a wave recorder on a moving ship, In Ocean Wave Spectra”, pages 203—218, Prentice Hall, New Jersey). Some distributional properties of the Cartwright’s power-of-cosine circular distribution will be discussed in this paper. Based on these properties, some characterizations of this distribution will be given using the truncated moment, order statistics and record values. [ABSTRACT FROM AUTHOR]

Ridge regression techniques have been extensively used to solve the multicollinearity problem for both linear and non-linear regression models since its inception. This paper studied different ridge regression t-type tests of the individual coefficients of a linear regression model. A simulation study has been conducted to evaluate the performance of the proposed tests with respect to their sizes and powers under different settings of the linear regression model. Our simulation results demonstrated that most of the proposed tests have sizes close to the 5% nominal level and all tests except tAKS, tkM2 and tkM9 have considerable gain in powers over the ordinary OLS t-type test. It is also observed that some of the proposed test statistics are performing better than the HK and HKB tests which are proposed some authors. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new bivariate control chart denoted by [ABSTRACT FROM AUTHOR]

The distributions of linear combinations, and ratios of random variables arise explicitly in many reliability problems. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this paper, the exact distributions of αX + βY, and X/ Y are derived when X, and V follow two of the most applied models in reliability. Computer programs for calculating the associated percentage points are also given. [ABSTRACT FROM AUTHOR]

The general linear regression model has been one of the most frequently used models over the years, with the ordinary least squares estimator (OLS) used to estimate its parameter. The problems of the OLS estimator for linear regression analysis include that of multicollinearity and outliers, which lead to unfavourable results. This study proposed a two-parameter ridge-type modified M-estimator (RTMME) based on the M-estimator to deal with the combined problem resulting from multicollinearity and outliers. Through theoretical proofs, Monte Carlo simulation, and a numerical example, the proposed estimator outperforms the modified ridge-type estimator and some other considered existing estimators., Competing Interests: The authors declare that they have no conflicts of interest., (Copyright © 2020 Adewale F. Lukman et al.)