TESTING INDEPENDENCE IN TIME SERIES VIA UNIVERSAL DISTRIBUTIONS OF PERMUTATIONS AND WORDS

2005 ◽  
Vol 15 (05) ◽  
pp. 1757-1765 ◽  
Author(s):  
CAMILLO CAMMAROTA ◽  
ENRICO ROGORA
Keyword(s):  
Time Series ◽  
General Framework ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Recursive Algorithm ◽  
Chi Square ◽  
Independent Sequence ◽  
Empirical Distributions ◽  
Testing Independence ◽  
Analysis Of Time Series

We study probability distributions of permutations and binary words, which arise in symbolic analysis of time series and their differences. Under the assumptions that the series is stationary and independent we show that these probability distributions are universal and we derive a recursive algorithm for computing the distribution of binary words. This provides a general framework for performing chi square tests of goodness of fit of empirical distributions versus universal ones. We apply these methods to analyze heartbeat time series; in particular, we measure the extent to which atrial fibrillation can be modeled as an independent sequence.

scholarly journals Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

2021 ◽  
Vol 2 (2) ◽  
pp. 60-67
Author(s):  
Rashidul Hasan Rashidul Hasan
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Model ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

scholarly journals Probabilistic Modeling of Monthly Temperature Historical Series in Mossoró, Northeastern Brazil

2018 ◽  
Vol 10 (12) ◽  
pp. 534
Author(s):  
Janilson Pinheiro de Assis ◽  
Roberto Pequeno de Sousa ◽  
Ben Deivide de Oliveira Batista ◽  
Paulo César Ferreira Linhares ◽  
Eudes de Almeida Cardoso ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Northeastern Brazil ◽  
Chi Square ◽  
Empirical Distributions ◽  
Monthly Temperature ◽  
Small Series ◽  
Pearson Type ◽  
Historical Series ◽  
Kolmogorov Smirnov ◽  
Von Mises

We fitted the following seven distribution probabilities to the data of monthly average temperature in Mossoró, northeastern Brazil: Normal, Log-Normal, Beta, Gamma, Log-Pearson (Type III), Gumbel, and Weibull. To assess the goodness of fit the empirical distributions to the theoretical distribution, we applied the tests of Kolmogorov-Smirnov, Chi-square, Cramer-von Mises, Anderson-Darling, Kuiper, and Logarithm of Maximum Likelihood, at 10% of probability. The temperature series were obtained from 1970 to 2007. The Normal distribution provided the best fit to the historical series of average monthly temperature. Although the Kolmogorov-Smirnov test showed a very high level of approval, which generated some uncertainty regarding the test criteria, it is the more recommended to studies with approximately symmetric data and small series.

scholarly journals Intercomparison of estimators of extreme value family of distributions for rainfall frequency analysis

MAUSAM ◽  
2022 ◽  
Vol 73 (1) ◽  
pp. 59-70
Author(s):  
N. VIVEKANANDAN
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Extreme Value ◽  
Qualitative Assessment ◽  
Likelihood Method ◽  
Extreme Value Analysis ◽  
Chi Square ◽  
Maximum Rainfall ◽  
Value Analysis ◽  
Family Of Distributions

Estimation of rainfall for a given return period is of utmost importance for planning and design of minor and major hydraulic structures. This can be achieved through Extreme Value Analysis (EVA) of rainfall by fitting Extreme Value family of Distributions (EVD) such as Generalized Extreme Value, Extreme Value Type-1, Extreme Value Type-2 and Generalized Pareto to the series of observed Annual 1-Day Maximum Rainfall (AMR) data. Based on the intended applications and the variate under consideration, Method of Moments (MoM), Maximum Likelihood Method (MLM) and L-Moments (LMO) are used for determination of parameters of probability distributions. The adequacy of fitting EVD to the AMR series was evaluated by quantitative assessment using Goodness-of-Fit (viz., Chi-square and Kolmogorov-Smirnov) and diagnostic test (viz., D-index) tests and qualitative assessment by the fitted curves of the estimated rainfall. The paper presents a study on intercomparison of EVD (using MoM, MLM and LMO) adopted in EVA of rainfall with illustrative example and the results obtained thereof. 

scholarly journals Assessing Goodness of Fit for Verifying Probabilistic Forecasts

Forecasting ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 763-773
Author(s):  
Tae-Ho Kang ◽  
Ashish Sharma ◽  
Lucy Marshall
Keyword(s):  
Goodness Of Fit ◽  
Integral Transformation ◽  
Southern Oscillation ◽  
Probability Distributions ◽  
Ensemble Prediction ◽  
Probabilistic Prediction ◽  
Test Statistic ◽  
Chi Square ◽  
Predicted Probability ◽  
Probabilistic Forecasts

The verification of probabilistic forecasts in hydro-climatology is integral to their development, use, and adoption. We propose here a means of utilizing goodness of fit measures for verifying the reliability of probabilistic forecasts. The difficulty in measuring the goodness of fit for a probabilistic prediction or forecast is that predicted probability distributions for a target variable are not stationary in time, meaning one observation alone exists to quantify goodness of fit for each prediction issued. Therefore, we suggest an additional dissociation that can dissociate target information from the other time variant part—the target to be verified in this study is the alignment of observations to the predicted probability distribution. For this dissociation, the probability integral transformation is used. To measure the goodness of fit for the predicted probability distributions, this study uses the root mean squared deviation metric. If the observations after the dissociation can be assumed to be independent, the mean square deviation metric becomes a chi-square test statistic, which enables statistically testing the hypothesis regarding whether the observations are from the same population as the predicted probability distributions. An illustration of our proposed rationale is provided using the multi-model ensemble prediction for El Niño–Southern Oscillation.

Goodness-of-Fit Tests for Probability Distributions and Spectral Distributions

1995 ◽  
Vol 9 (1) ◽  
pp. 27-37 ◽  
Author(s):  
T. W. Anderson
Keyword(s):  
Least Squares ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Close Friend ◽  
Columbia University ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Spectral Distributions ◽  
One Year ◽  
Promising Student

In the fall of 1948 in my course on Least Squares in the Department of Mathematical Statistics at Columbia University (and in the spring in Correlation and Chi-Square), I was particularly impressed by one of the students— Gerald J. Lieberman. I was disappointed that this promising student left Columbia after one year, but it was not long until our paths met again. It is a pleasure to dedicate this paper to my colleague and close friend!

scholarly journals Gaussian and Non-Gaussian Autoregressive Time Series Models with Rainfall Data

2019 ◽  
Vol 9 (1) ◽  
pp. 6699-6704
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Time Series Data ◽  
Autoregressive Models ◽  
Annual Rainfall ◽  
Series Data ◽  
Time Series Models ◽  
Chi Square ◽  
Autoregressive Time Series ◽  
Non Gaussian

The Gaussian and non- Gaussian autoregressive models are used in this paper for analyzing time series data. The autoregressive time series models with various distributions are considered here for analyzing the annual rainfall of Punjab, India. Three different types of autoregressive models are applied here for analyzing data namely autoregressive model with Gaussian, Gamma and Laplace distribution. For the goodness of fit the chi - square test is applied and the best fitted distribution is obtained for the data. Next the stationarity of data is checked, after that models are applied on data for comparing three distributions of AR models and lastly the best fitted model is obtained. The residual checking of selected model is also discussed and forecast the best fitted model based on simulated response comparison.

Correlation in the heart rate data

1998 ◽  
Vol 2 ◽  
pp. 141-148
Author(s):  
J. Ulbikas ◽  
A. Čenys ◽  
D. Žemaitytė ◽  
G. Varoneckas
Keyword(s):  
Nonlinear Dynamics ◽  
Experimental Data ◽  
Heart Rate ◽  
Time Series ◽  
Cardiovascular Function ◽  
Statistical Properties ◽  
Rate Data ◽  
Heart Rate Data ◽  
Dynamical Nature ◽  
Analysis Of Time Series

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed.

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