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.

Probability Functions which are Proportional to Characteristic Functions and the Infinite Divisibility of the von Mises Distribution

1975 ◽  
Vol 12 (S1) ◽  
pp. 19-28 ◽  
Author(s):  
Toby Lewis
Keyword(s):  
Continuous Distribution ◽  
Random Variables ◽  
Discrete Distribution ◽  
Infinite Divisibility ◽  
Reciprocal Relationship ◽  
Characteristic Functions ◽  
Von Mises Distribution ◽  
Infinitely Divisible ◽  
Von Mises ◽  
Divisibility Properties

Reciprocal pairs of continuous random variables on the line are considered, such that the density function of each is, to within a norming factor, the characteristic function of the other. The analogous reciprocal relationship between a discrete distribution on the line and a continuous distribution on the circle is also considered. A conjecture is made regarding infinite divisibility properties of such pairs of random variables. It is shown that the von Mises distribution is infinitely divisible for sufficiently small values of the concentration parameter.

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 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 A Comparison of Asymptotic and Bootstrapping Approach in Constructing Confidence Interval of the Concentration Parameter in von Mises Distribution

2019 ◽  
Vol 48 (5) ◽  
pp. 1151-1156
Author(s):  
Nor Hafizah Moslim ◽  
Yong Zulina Zubairi ◽  
Abdul Ghapor Hussin ◽  
Siti Fatimah Hassan ◽  
Nurkhairany Amyra Mokhtar
Keyword(s):  
Confidence Interval ◽  
Von Mises Distribution ◽  
Concentration Parameter ◽  
Von Mises

An extension of the von mises distribution

1982 ◽  
Vol 11 (15) ◽  
pp. 1695-1706 ◽  
Author(s):  
E.A. Yfantis ◽  
L.E. Borgman
Keyword(s):  
Von Mises Distribution ◽  
Von Mises

Error-in-variables model of Malacca wind direction data with the von Mises distribution in southwest monsoon

2021 ◽  
Vol 15 (9) ◽  
pp. 471-479
Author(s):  
Nurkhairany Amyra Mokhtar ◽  
Basri Badyalina ◽  
Kerk Lee Chang ◽  
Fatin Farazh Ya'acob ◽  
Ahmad Faiz Ghazali ◽  
...  
Keyword(s):  
Wind Direction ◽  
Southwest Monsoon ◽  
Von Mises Distribution ◽  
Error In Variables ◽  
Von Mises

scholarly journals Distributions with complete monotone derivative and geometric infinite divisibility

1990 ◽  
Vol 22 (3) ◽  
pp. 751-754 ◽  
Author(s):  
R. N. Pillai ◽  
E. Sandhya
Keyword(s):  
Infinite Divisibility ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Proper Subclass ◽  
Geometric Infinite Divisibility

It is shown that a distribution with complete monotone derivative is geometrically infinitely divisible and that the class of distributions with complete monotone derivative is a proper subclass of the class of geometrically infinitely divisible distributions.

scholarly journals STATISTICAL MODEL FOR THE RELATIONSHIP BETWEEN MAIZE KERNEL ORIENTATION AND SEED LEAF AZIMUTH

2015 ◽  
Vol 52 (3) ◽  
pp. 359-370
Author(s):  
ADRIAN KOLLER ◽  
GUILHERME TORRES ◽  
MICHAEL BUSER ◽  
RANDY TAYLOR ◽  
BILL RAUN ◽  
...  
Keyword(s):  
Simulation Models ◽  
Circular Statistics ◽  
Von Mises Distribution ◽  
Canopy Closure ◽  
Canopy Architecture ◽  
Maize Kernel ◽  
Angular Data ◽  
Significant Yield ◽  
Von Mises ◽  
The Relationship

SUMMARYHand-planted plots of across-row-oriented corn seeds (Zeamays L.) produce highly structured leaf canopies and have shown significant yield advantage over randomly planted plots in prior studies. For further investigation of the phenomenon by simulation, the objective of this study was to develop a probabilistic model for the correlation between seed orientation and initial plant orientation. In greenhouse trials, the azimuthal orientation of kernels of four different hybrids was recorded at planting. At collar setting of the seed leaf, the orientation of the seed leaf was determined and the angular data subjected to the analytical methods of circular statistics. The results indicate that the correlation between seed azimuth and seed leaf azimuth can be described by a von Mises distribution. The probabilistic seed to seed leaf azimuth model described herein may be implemented in simulation models to investigate the effect of canopy architecture, canopy closure and light interception efficiency of corn under conditions of seed oriented planting.

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