scholarly journals On the approximation of the concentration parameter for von Mises distribution

2017 ◽  
Vol 13 (4-1) ◽  
pp. 390-393
Author(s):  
Nor Hafizah Moslim ◽  
Yong Zulina Zubairi ◽  
Abdul Ghapor Hussin ◽  
Siti Fatimah Hassan ◽  
Rossita Mohamad Yunus
Keyword(s):  
Goodness Of Fit ◽  
Von Mises Distribution ◽  
Concentration Parameter ◽  
Normal Behavior ◽  
Kolmogorov Smirnov ◽  
Asymptotic Normal ◽  
Level Of Significance ◽  
Von Mises ◽  
Two Parameters ◽  
Relationship Of

The von Mises distribution is the ‘natural’ analogue on the circle of the Normal distribution on the real line and is widely used to describe circular variables. The distribution has two parameters, namely mean direction,  and concentration parameter, κ. Solutions to the parameters, however, cannot be derived in the closed form. Noting the relationship of the κ to the size of sample, we examine the asymptotic normal behavior of the parameter. The simulation study is carried out and Kolmogorov-Smirnov test is used to test the goodness of fit for three level of significance values. The study suggests that as sample size and concentration parameter increase, the percentage of samples follow the normality assumption increase. 

scholarly journals Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data

2003 ◽  
Vol 33 (2) ◽  
pp. 365-381 ◽  
Author(s):  
Vytaras Brazauskas ◽  
Robert Serfling
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Efficient Estimation ◽  
Small Samples ◽  
Robust Estimators ◽  
Trade Offs ◽  
Pareto Model ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

Weibull diameter distributions for mixed stands of western conifers

1983 ◽  
Vol 13 (1) ◽  
pp. 85-88 ◽  
Author(s):  
Susan N. Little
Keyword(s):  
Goodness Of Fit ◽  
Test Group ◽  
Stand Age ◽  
Weibull Function ◽  
Prediction Equations ◽  
Mixed Stands ◽  
Forest Inventories ◽  
Kolmogorov Smirnov ◽  
Level Of Significance ◽  
Diameter Distributions

The three-parameter Weibull function met specified standards for goodness of fit as a model for the diameter distributions of mixed stands of western hemlock and Douglas-fir. Weibull distributions estimated by maximum likelihood (MLE) fit 80 of 83 observed diameter distributions at the α = 0.20 level of significance by the Kolmogorov–Smirnov test. Weibull parameter prediction equations were developed by regressing characteristics of 42 stands against MLE of the parameters. The Weibull diameter distributions predicted from stand age, mean diameter, mean height, and trees per acre (1 a = 100 m2) fit 39 of 41 observed distributions in the test group at the α = 0.20 level of significance. These results compared favorably with those found for various forest types by other authors. These prediction equations will prove useful in stand modeling and in updating forest inventories.

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.

Reliability Analysis of the Hydro-System of Excavator SchRs 800 Using Weibull Distribution

2015 ◽  
Vol 806 ◽  
pp. 173-180 ◽  
Author(s):  
Predrag Dašić ◽  
Milutin Živković ◽  
Marina Karić
Keyword(s):  
Weibull Distribution ◽  
Reliability Analysis ◽  
Goodness Of Fit ◽  
Weibull Model ◽  
Reliability Model ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Von Mises

In this paper is given the use Weibull distribution (WD) as theoretical reliability model for analysis of the hydro-system of excavator SchRs 800, which is accepted on the basis of Pearson (χ2), Kolmogorov-Smirnov (KS) and Cramér-von Mises (CvM) goodness-of-fit tests. The time of work without failure of the hydro-system of excavator SchRs 800 for accepted Weibull model of reliability for probability of 50 % is T50%=0.3417⋅103[h], for probability of 80 % is T80%=0.1884⋅103[h] and for probability of 90% is T90%=0.127⋅103[h].

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

scholarly journals Construction of Confidence Interval of the Parameter in Von Mises Distribution using Bootstrap Methods

2020 ◽  
pp. 1-7
Author(s):  
Nor Hafizah Moslim ◽  
Yong Zulina Zubairi ◽  
Abdul Ghapor Hussin ◽  
Siti Fatimah Hassan ◽  
Nurkhairany Amyra Mokhtar
Keyword(s):  
Confidence Interval ◽  
Bootstrap Method ◽  
Von Mises Distribution ◽  
Concentration Parameter ◽  
Statistical Inferences ◽  
Wide Range ◽  
Expected Length ◽  
Computer Based ◽  
Von Mises ◽  
Percentile Bootstrap

Bootstrap method is a computer-based technique for making certain kind of statistical inferences which can simplify the often intricate calculations of traditional statistical theory. Recently, bootstrapping has been widely used for the parameter estimation of linear data. In this paper, we consider bootstrapping methods in the construction of the confidence interval of concentration parameter, for the von Mises distribution. The performances of confidence interval based on percentile bootstrap, bootstrap-t and calibration bootstrap are evaluated via simulation study. The numerical results found that confidence interval based on the calibration bootstrap is good in terms of coverage probability. Meanwhile, confidence interval based on the bootstrap-t method has a shorter expected length. The confidence intervals were illustrated using daily wind direction data recorded at maximum wind speed for four stations in Malaysia. From point estimates of the concentration parameter and the respective confidence interval, we note that the method works well for a wide range of values. The implication of the study is that confidence interval of the concentration parameter can be obtained using bootstrap as it provides good estimates. Keywords: bootstrap-t; calibration bootstrap; concentration parameter; percentile bootstrap; von Mises distribution

scholarly journals On the infinite divisibility of the von Mises distribution

1976 ◽  
Vol 22 (3) ◽  
pp. 332-342
Author(s):  
Toby Lewis
Keyword(s):  
Infinite Divisibility ◽  
Von Mises Distribution ◽  
Type Condition ◽  
Infinitely Divisible ◽  
Concentration Parameter ◽  
Von Mises

AbstractIt is shown, by use of a Bochner-type condition for infinite divisibility, that the von Mises distribution is infinitely divisible for some values of the concentration parameter k, certainly for k < 0.16.

scholarly journals Performances of Shannon’s Entropy Statistic in Assessment of Distribution of Data

2017 ◽  
Vol 28 (2) ◽  
pp. 30-42 ◽  
Author(s):  
Lorentz Jäntschi ◽  
Sorana D. Bolboacă
Keyword(s):  
Experimental Data ◽  
Goodness Of Fit ◽  
Error Function ◽  
Shannon’S Entropy ◽  
Goodness Of Fit Test ◽  
Shannon's Entropy ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

AbstractStatistical analysis starts with the assessment of the distribution of experimental data. Different statistics are used to test the null hypothesis (H0) stated as Data follow a certain/specified distribution. In this paper, a new test based on Shannon’s entropy (called Shannon’s entropy statistic, H1) is introduced as goodness-of-fit test. The performance of the Shannon’s entropy statistic was tested on simulated and/or experimental data with uniform and respectively four continuous distributions (as error function, generalized extreme value, lognormal, and normal). The experimental data used in the assessment were properties or activities of active chemical compounds. Five known goodness-of-fit tests namely Anderson-Darling, Kolmogorov-Smirnov, Cramér-von Mises, Kuiper V, and Watson U2 were used to accompany and assess the performances of H1.

scholarly journals Modeling of short duration extreme rainfall events over Lower Yamuna Catchment

MAUSAM ◽  
2022 ◽  
Vol 63 (3) ◽  
pp. 391-400
Author(s):  
MEHFOOZ ALI ◽  
SURINDER KAUR ◽  
S.B. TYAGI ◽  
U.P. SINGH
Keyword(s):  
Short Duration ◽  
Goodness Of Fit ◽  
Extreme Rainfall ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Extreme Rainfall Events ◽  
Rainfall Events ◽  
Kolmogorov Smirnov ◽  
Level Of Significance ◽  
Made In

Short duration rainfall estimates and their intensities for different return periods are required for many purposes such as for designing flood for hydraulic structures, urban flooding etc. An attempt has been made in this paper to Model extreme rainfall events of Short Duration over Lower Yamuna Catchment. Annual extreme rainfall series and their intensities were analysed using EVI distribution for rainstorms of short duration of 5, 10, 15, 30, 45 & 60 minutes and various return periods have been computed. The Self recording rainguage (SRRGs) data for the period 1988-2009 over the Lower Yamuna Catchment (LYC) have been used in this study. It has been found that EVI distribution fits well, tested by Kolmogorov-Smirnov goodness of fit test at 5 % level of significance for each of the station.

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