Abstract
A non-Gaussian model as a function of Gaussian process is developed in this paper for Indian monsoon rainfall time series. The functions of a Gaussian process are the Hermite polynomials. The unknown coefficients of the Hermite polynomials are found with the help of the first four moments of the given data. Since the probability density function of the Gaussian process is known, the non-Gaussian density function for the rainfall process is found by using the transformation on the known Gaussian density function numerically. Sample histogram of the data and the non-Gaussian density function are compared graphically along with the Gaussian density function. This clearly justifies that the non-Gaussian density better compares with the data distribution. This exercise has been done on the four broad regions of India identified by Indian Meteorological Department (IMD) and also for one subdivision of Karnataka. It has been observed that at 5% significance level, this model is able to reproduce the probability structure of the rainfall time series at different spatial scales studied.
Highlights
In many applications, we come across non-Gaussian time series such as rainfall, earthquake etc
The modeled non-Gaussian one dimensional probability density function (PDF) of x for all possible real roots is compared with the sample PDF to arrive at the final conclusion of selection of ai’s
The model developed for all India SWM rainfall data, its broad regions and a subdivision is a non-Gaussian model
Summary
We come across non-Gaussian time series such as rainfall, earthquake etc. Modeling of such time series will be of at most importance. Most commonly used assumption for this kind of series would be stationarity and Gaussianness. The advantage of this assumption will be using Gaussian model and its characteristics. When any time series is given it is assumed that the data is stationary and Gaussian to make further analysis simple. If a nonGaussian model is to be proposed for the given time series, it is preferable to completely
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