Related papers: Two samples test for discrete power-law distributi…
Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data…
It is well known that random multiplicative processes generate power-law probability distributions. We study how the spatio-temporal correlation of the multipliers influences the power-law exponent. We investigate two sources of the time…
More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
We present the results of a large number of simulation studies regarding the power of various non-parametric two-sample tests for multivariate data. This includes both continuous and discrete data. In general no single method can be relied…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…
Correlations in music that exist within its waveform are studied. Monophonic wave files of random music are generated and the probability distribution function of time interval between large signal values is analyzed. A power law behavior…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic is presented for the case of the power law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…
Enduring violent conflicts are interrupted by lulls without violence. Studies of interevent times found power law distributions based on coarse-grained data with a resolution of one day. Fine-grained data of violence with a resolution of…
A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the…
The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional…
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…
Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…