This paper describes regime-switching, full range of shape changing distributions (multimodalities), and cycles traits that were characterized by time-varying series via Weibull distributional noise for time series with fluctuations and long-memory. We developed and established a Weibull Mixture Autoregressive model of k-regimes via with Expectation-Maximization (EM) algorithm adopted as parameter estimation technique. The ergodic process for the model was ascertained via the maximized derivation of the absolute value of the subtraction of its likelihood from its expected likelihood.
The purpose of this essay is to act as a supplement for students who wish to reinforce their knowledge of the quadratic formula. It is not intended to be used as a primary source of education. If so, it should be used in collaboration with an expert of mathematics. This essay focuses primarily on the ways a quadratic equation can be solved. This includes an explanation of factoring, completing the square, the quadratic formula, and references to graphical approaches and analysis.
We provide a generalized maximum entropy method and its application to the Agronomic dataset. Errors of deviation are shown with the analysis of variance on the entropy method. Multi-collinearity is one of the major problems of regression analysis. Based on the maximum entropy method, we gave a better estimate than the traditional robust regression of four independent variables from an Agronomic dataset. From the generalized maximum entropy method, we showed the relationship between the dependent and independent variables. Also, we provided a diagnostic fit for the dependent variable to support the theoretical analysis.
The square root transformation of the error component of the additive time series model was studied. The distribution of the transformed error component was established and shown that it is a proper probability density function. The properties of the distribution were investigated. It was shown that the mean of the transformed series is equal to one while the mean of the original series = 0 for . Also, the variance of the transformed was established and given as and is four times that of the original series for to one decimal place. The transformed series is normally distributed for .
Mathematical series play an important role in various aspects of our life and help to predict, evaluate and monitor the outcome of a situation in order to pass decision. The purpose of this paper is to develop a new kind of series and the sum or deduction of two terms of which fractionally cancel in order to get the cancellation result . let for all and let such that and then .
