13,244 research outputs found
The Radio and Gamma-Ray Luminosities of Blazars
Based on the -ray data of blazars in the third EGRET catalog and
radio data at 5 GHz, we studied the correlation between the radio and
-ray luminosities using two statistical methods. The first method was
the partial correlation analysis method, which indicates that there exist
correlations between the radio and -ray luminosities in both high and
low states as well as in the average case.
The second method involved a comparison of expected -ray luminosity
distribution with the observed data using the Kolmogorov--
Smirnov (KS) test. In the second method, we assumed that there is a
correlation between the radio and -ray luminosities and that the
-ray luminosity function is proportional to the radio luminosity
function. The KS test indicates that the expected gamma-ray luminosity
distributions are consistent with the observed data in a reasonable parameter
range. Finally, we used different -ray luminosity functions to estimate
the possible 'observed'
-ray luminosity distributions by GLAST.Comment: 8 pages, 4 figures, one table, PASJ, 53 (2001
KOLMOGOROV-SMIRNOV TYPE TESTS UNDER SPATIAL CORRELATIONS
Kolmogorov-Smirnov test is a non-parametric hypothesis test that measures the probability of deviations, that the interested univariate random variable is drawn from a pre-specified distribution (one-sample KS) or has the same distribution as a second random variable (twosample KS). The test is based on the measure of the supremum (greatest) distance between an empirical distribution function (EDF) and a pre-specified cumulative distribution function (CDF) or the largest distance between two EDFs. KS test has been widely adopted in statistical analysis due to its virtue of more general assumptions compared to parametric test like t-test. In addition, the p-value derived from the KS test is more robust and distribution-free for a large class of random variables. However, the fundamental assumption of independence is usually overlooked and may potentially cause inaccurate inferences. The KS test in its original form assumes the interested random variable to be independently distributed while it’s not true in a lot of nature datasets, especially when we are dealing with more complicated situations like imgage analysis, geostatistical which may involve spatial dependence. I proposed a modified KS test with adjustment via spatial correlation. The dissertation concerns the following three aims. First, I conducted a systematical review on the KS test, the Cramer von Mise test, the Anderson-Darling test and the Chi-square test and evaluate their performance under normal distributions, Weibull distributions and multinomial distributions. In the review, I also studied how these tests perform when random variables are correlated. Second, I proposed a modified KS test that corrects the bias in estimating CDF/EDF when spatial dependence exists and calculate the informative sample size. Finally, I conducted a revisit analysis of coronary flow reserve and pixel distribution of coronary flow capacity by Kolmogorov-Smirnov with spatial correction to evaluate the efficiency of dipyridamole and regadenoson
On Misuses of the Kolmogorov–Smirnov Test for One-Sample Goodness-of-Fit
The Kolmogorov–Smirnov (KS) test is one of the most popular goodness-of-fit tests for comparing a sample with a hypothesized parametric distribution. Nevertheless, it has often been misused. The standard one-sample KS test applies to independent, continuous data with a hypothesized distribution that is completely specified. It is not uncommon, however, to see in the literature that it was applied to dependent, discrete, or rounded data, with hypothesized distributions containing estimated parameters. For example, it has been discovered multiple times that the test is too conservative when the parameters are estimated. We demonstrate misuses of the one-sample KS test in three scenarios through simulation studies: 1) the hypothesized distribution has unspecified parameters; 2) the data are serially dependent; and 3) a combination of the first two scenarios. For each scenario, we provide remedies for practical applications
Statistical properties of volatility return intervals of Chinese stocks
The statistical properties of the return intervals between
successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain
threshold are carefully studied. The Kolmogorov-Smirnov (KS) test shows
that 12 stocks exhibit scaling behaviors in the distributions of for
different thresholds . Furthermore, the KS test and weighted KS test shows
that the scaled return interval distributions of 6 stocks (out of the 12
stocks) can be nicely fitted by a stretched exponential function
with
under the significance level of 5%, where is
the mean return interval. The investigation of the conditional probability
distribution and the mean conditional return interval
after a cluster of intervals and the fluctuation
using detrended fluctuation analysis and find that long-term memory also exists
in the volatility return intervals.Comment: 8 pages, 8 figure
A Kolmogorov-Smirnov test for the molecular clock on Bayesian ensembles of phylogenies
Divergence date estimates are central to understand evolutionary processes
and depend, in the case of molecular phylogenies, on tests of molecular clocks.
Here we propose two non-parametric tests of strict and relaxed molecular clocks
built upon a framework that uses the empirical cumulative distribution (ECD) of
branch lengths obtained from an ensemble of Bayesian trees and well known
non-parametric (one-sample and two-sample) Kolmogorov-Smirnov (KS)
goodness-of-fit test. In the strict clock case, the method consists in using
the one-sample Kolmogorov-Smirnov (KS) test to directly test if the phylogeny
is clock-like, in other words, if it follows a Poisson law. The ECD is computed
from the discretized branch lengths and the parameter of the expected
Poisson distribution is calculated as the average branch length over the
ensemble of trees. To compensate for the auto-correlation in the ensemble of
trees and pseudo-replication we take advantage of thinning and effective sample
size, two features provided by Bayesian inference MCMC samplers. Finally, it is
observed that tree topologies with very long or very short branches lead to
Poisson mixtures and in this case we propose the use of the two-sample KS test
with samples from two continuous branch length distributions, one obtained from
an ensemble of clock-constrained trees and the other from an ensemble of
unconstrained trees. Moreover, in this second form the test can also be applied
to test for relaxed clock models. The use of a statistically equivalent
ensemble of phylogenies to obtain the branch lengths ECD, instead of one
consensus tree, yields considerable reduction of the effects of small sample
size and provides again of power.Comment: 14 pages, 9 figures, 8 tables. Minor revision, additin of a new
example and new title. Software:
https://github.com/FernandoMarcon/PKS_Test.gi
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