An approach to Stochastic Process using Quasi-Arithmetic Means
نویسندگان
چکیده
Probability distributions are central tools for probabilistic modeling in data mining. In functional data analysis (FDA) they are weakly studied in the general case. In this paper we discuss a probability distribution law for functional data considered as stochastic process. We define first a new kind of stationarity linked t o the Archimedean copulas, and then we build a probability distribution using jointly the Quasi-arithmetic means and the generators of Archimedean copulas. We also study some properties of this new mathematical tool.
منابع مشابه
Confidence Interval Estimation of the Mean of Stationary Stochastic Processes: a Comparison of Batch Means and Weighted Batch Means Approach (TECHNICAL NOTE)
Suppose that we have one run of n observations of a stochastic process by means of computer simulation and would like to construct a condifence interval for the steady-state mean of the process. Seeking for independent observations, so that the classical statistical methods could be applied, we can divide the n observations into k batches of length m (n= k.m) or alternatively, transform the cor...
متن کاملDynamical Control of Computations Using the Family of Optimal Two-point Methods to Solve Nonlinear Equations
One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...
متن کاملQuasi-arithmetic means of covariance functions with potential applications to space-time data
The theory of quasi-arithmetic means is a powerful tool in the study of covariance functions across space-time. In the present study we use quasiarithmetic functionals to make inferences about the permissibility of averages of functions that are not, in general, permissible covariance functions. This is the case, e.g., of the geometric and harmonic averages, for which we obtain permissibility c...
متن کاملAn extension of stochastic differential models by using the Grunwald-Letnikov fractional derivative
Stochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach b...
متن کاملA new approach to enhance final surface quality in drilling operation: evaluation of using alumina micro-particle additives on oil-water emulsion cutting fluid
Reaming is a common finishing process for improving the drilled holes surface quality. Choosing an appropriate finishing method in drilling process has a significant effect on the surface quality of holes and in decreasing the process total cost and time. In this study, four similar holes were drilled on the AISI 4340 workpiece with different two pair feed rates. The drilling process was perfor...
متن کامل