scholarly journals Goodness-of-fit Testing for Left-truncated Two-parameter Weibull Distributions with Known Truncation Point

2016 ◽  
Vol 45 (3) ◽  
pp. 15-42 ◽  
Author(s):  
Ayse KIZILERSU ◽  
Markus Kreer ◽  
Anthony W. Thomas
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Brownian Bridge ◽  
Critical Values ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Weibull Parameters ◽  
Kolmogorov Smirnov ◽  
Power Testing

The left-truncated Weibull distribution is used in life-time analysis, it has many applications ranging from financial market analysis and insurance claims to the earthquake inter-arrival times.We present a comprehensive analysis of the left-truncated Weibull distribution when the shape, scale or both parameters are unknown and they are determined from the data using the maximum likelihood estimator. We demonstrate that if both the Weibull parameters are unknown then there are sets of sample configurations, with measure greater than zero, for which the maximum likelihood equations do not possess non trivial solutions. The modified critical values of the goodness-of-fit test from the Kolmogorov-Smirnov test statistic when the parameters are unknown are obtained from a quantile analysis. We find that the critical values depend on sample size and truncation level, but  not on the actual Weibull parameters.  Confirming this behavior, we present a complementary analysis using the Brownian bridge approach as an asymptotic limit of the Kolmogorov-Smirnov statistics and find that both approaches are in good agreement. A power testing is performed for our Kolmogorov-Smirnov goodness-of-fit test and  the issues related to the left-truncated data are discussed. We conclude the paper by showing the importance of left-truncated Weibulldistribution hypothesis testing on  the duration times of failed marriages in the US, worldwide terrorist attacks, waiting times between stock market orders, and time intervals of radioactive decay.

AN ALTERNATIVE TEST FOR UNIFORMITY

2009 ◽  
Vol 16 (04) ◽  
pp. 343-356 ◽  
Author(s):  
ZHENMIN CHEN ◽  
CHUNMIAO YE
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Integral Transformation ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Underlying Distribution ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Alternative Test ◽  
Smirnov Test

Improving power of goodness-of-fit tests is an important research topic in statistics. The goal of the goodness-of-fit test is to check whether the underlying probability distribution, from which a sample is drawn, differs from a hypothesized distribution. Numerous research papers have been published in this area. It has been shown that the power of the existing goodness-of-fit tests in the literature is unsatisfactory when the alternative distributions are of V-shape or when the sample sizes are small. This motivates the development of more powerful test statistics. In this research, a new test statistic is proposed. The result can be used to test whether the underlying probability distribution differs from a uniform distribution. By applying the probability integral transformation, the proposed test statistic can be used to check whether the underlying distribution differs from any hypothesized distribution. The performance of the method proposed in this research is compared with the Kolmogorov–Smirnov test, which is a widely adopted statistical test in the literature. It has been shown that the test proposed in this proposal is more powerful than the Kolmogorov–Smirnov test in some cases.

scholarly journals A powerful goodness-of-fit test for Lindley distribution with application to real data

2021 ◽  
pp. 761-769
Author(s):  
Hadi Alizadeh Noughabi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Critical Points ◽  
Goodness Of Fit ◽  
Real Data ◽  
Reliability Model ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Lindley Distribution

The Lindley distribution may serve as a useful reliability model. Applications of this distribution are presented in statistical literature. In this article, a powerful goodness of fit test for the Lindley distribution is proposed. In order to compute the proposed test statistic, we use the maximum likelihood estimate (MLE) suggested by Ghitany et al. (2008), which is simple explicit estimator. By Monte Carlo simulation, critical points of the proposed test statistic for different sample sizes are obtained. Power values of the proposed test are compared with the competing tests against various alternatives via simulations. Finally, two real data are presented and analyzed.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

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