Characterization of maximum probability points in the Multivariate Hypergeometric distribution

2000 ◽  
Vol 50 (1) ◽  
pp. 39-47 ◽  
Author(s):  
F. Requena ◽  
N.Martin Ciudad
1976 ◽  
Vol 13 (04) ◽  
pp. 795-797 ◽  
Author(s):  
Jean Chesson

Selective predation is an example of biased sampling which gives rise to a non-central multivariate hypergeometric distribution. The probability distribution function of this distribution is derived.


Author(s):  
Navaneethakrishna Makaram ◽  
Ramakrishnan Swaminathan

Exercise-induced muscle damage is a condition which results in the loss of muscle function due to overexertion. Muscle fatigue is a precursor of this phenomenon. The characterization of muscle fatigue plays a crucial role in preventing muscle damage. In this work, an attempt is made to develop signal processing methods to understand the dynamics of the muscle’s electrical properties. Surface electromyography signals are recorded from 50 healthy adult volunteers under dynamic curl exercise. The signals are preprocessed, and the first difference signal is computed. Furthermore, ascending and descending slopes are used to generate a binary sequence. The binary sequence of various motif lengths is analyzed using features such as the average symbolic occurrence, modified Shannon entropy, chi-square value, time irreversibility, maximum probability of pattern and forbidden pattern ratio. The progression of muscle fatigue is assessed using trend analysis techniques. The motif length is optimized to maximize the rho value of features. In addition, the first and the last zones of the signal are compared with standard statistical tests. The results indicate that the recorded signals differ in both frequency and amplitude in both inter- and intra-subjects along the period of the experiment. The binary sequence generated has information related to the complexity of the signal. The presence of more repetitive patterns across the motif lengths in the case of fatigue indicates that the signal has lower complexity. In most cases, larger motif length resulted in better rho values. In a comparison of the first and the last zones, most of the extracted features are statistically significant with p < 0.05. It is observed that at the motif length of 13 all the extracted features are significant. This analysis method can be extended to diagnose other neuromuscular conditions.


1976 ◽  
Vol 13 (4) ◽  
pp. 795-797 ◽  
Author(s):  
Jean Chesson

Selective predation is an example of biased sampling which gives rise to a non-central multivariate hypergeometric distribution. The probability distribution function of this distribution is derived.


2016 ◽  
Vol 9 (3) ◽  
pp. 14-33
Author(s):  
Dirk Tasche

Premium Bonds sold by the UK National Savings and Investments (NS&I) agency are the possibly most popular example of lottery bonds. Premium Bonds holders renounce interest payments but instead participate in a lottery which distributes the equivalent of aggregate interest payments among them. While the random mechanism used in the lottery is well-documented the details of how to determine the probability distribution of a single bond holder's lottery prizes seem to be less well-known. We observe that the lottery prizes distribution is a multivariate hypergeometric distribution and discuss how to exactly calculate its probability masses as well as how to approximate the distribution by means of the Panjer recursion and Fourier transforms. We find that there are good reasons to prefer the approximations based on Panjer recursionor Fourier transforms to exact calculation of the lottery prize value distribution.


Sign in / Sign up

Export Citation Format

Share Document