### Table 2: Parameters of the negative binomial distributions for the frame size in Table 1.

2001

"... In PAGE 15: ... As a discrete version of the gamma distribution, let us assume that the distribu- tion of the frame size is negative binomial whose parameters are determined from the mean and variance of the actual data given in Table 1. Thus the probability generation functions for the frame size are given by with parameters given in Table2 . We also assume that cells are transmitted on a 10 Mbps channel, which corresponds to p = 2,350 cells/sec.... ..."

### Table 1. Table 1. Common distributions in F Density Moment Generating Function Mixing parameter

"... In PAGE 6: ... These are the normal, binomial, Poisson, negative binomial, generalized hyperbolic secant and gamma families of distributions. As it is evident from Table1 , the class F is di erent than Morris apos; NEF-QVF because, for example, does not contain the binomial distribution with parameter p. However, it contains all the generalized Poisson, binomial and negative binomial distributions, which have many important applications in risk theory, reliability and ecology.... In PAGE 7: ...a discrete distribution. The last three generalized distributions in Table1 correspond to cases in which K is drawn from a Poisson, binomial or negative binomial density respectively. See Douglas (1980) for a detailed account.... In PAGE 11: ... Identi ability for normal mixtures has been shown again by Teicher (1961), whereas for the logistic and Double exponential densities identi ability is straightforward using a Laplace transformation. Therefore, at least for the densities in Table1 we have results to guarantee a unique g( ). The algorithms in Appendix provide samples from unimodal densities.... ..."

### Table 1 Negative Binomial parameters of the multiplicity distributions.

### Table 2: Estimation using Negative Binomial Regression

in Abstract

"... In PAGE 7: ... We performed a negative binomial regression because the dependent variable (number of worms or number of variants released per month) fit well the negative binomial distribution. The results of the regression are reported in Table2 , column 2. Only the coefficients on dummy for FastTrack and eDonkey networks turned out to be significant predic- tors of worm count8.... In PAGE 7: ... Surprisingly, the coefficient on number of users was insignificant. A similar trend was observed for variant count data ( Table2 , column 3). An implicit assumption in the above estimation was that worm writers are focused only on P2P networks and respond directly to change in user population.... ..."

### Table 2: Estimation using Negative Binomial Regression

"... In PAGE 7: ... We performed a negative binomial regression because the dependent variable (number of worms or number of variants released per month) fit well the negative binomial distribution. The results of the regression are reported in Table2 , column 2. Only the coefficients on dummy for FastTrack and eDonkey networks turned out to be significant predic- tors of worm count8.... In PAGE 7: ... Surprisingly, the coefficient on number of users was insignificant. A similar trend was observed for variant count data ( Table2 , column 3). An implicit assumption in the above estimation was that worm writers are focused only on P2P networks and respond directly to change in user population.... ..."

### Table 2: Estimator for negative binomial distribution with x = 3

### Table 2: Estimator for negative binomial distribution with x = 3

### Table 5. Results of Curve Fitting for Number of Failures per Mission. Best Chi-sq Parameter Parameter Std

1996

"... In PAGE 9: ... In order to identify a distribution for the number of failures per mission, the chi-square goodness-of-fit test was applied to three discrete distributions: the binomial, Poisson, and negative binomial. In all cases, the nega- tive binomial was the only acceptable fit with the pa- rameter values as shown in Table5 . However, for the Wing TPS, the large chi-square value indicates the fit was marginal.... ..."

Cited by 6

### Table 5. Results of Curve Fitting for Number of Failures per Mission. Best Chi-sq Parameter Parameter Std

"... In PAGE 9: ... In order to identify a distribution for the number of failures per mission, the chi-square goodness-of-fit test was applied to three discrete distributions: the binomial, Poisson, and negative binomial. In all cases, the nega- tive binomial was the only acceptable fit with the pa- rameter values as shown in Table5 . However, for the Wing TPS, the large chi-square value indicates the fit was marginal.... ..."

### Table 2. Pdf apos;s, Factorial Moments, and Equivalent Density Functions for Some Discrete Random Variables Factorial Moments

1989

"... In PAGE 5: ... 1(b), which is more appropriate for the operation of real photodetectors. This operation leads to the distributions presented in Table2 , in which the corresponding factorial moments are also given. Note that the factorial moments in Table 2 are identical to the direct moments of the correspond- ing continuous distributions in Table 1, as noted in Section 2.... In PAGE 5: ... This operation leads to the distributions presented in Table 2, in which the corresponding factorial moments are also given. Note that the factorial moments in Table2 are identical to the direct moments of the correspond- ing continuous distributions in Table 1, as noted in Section 2. The exception is the noncentral negative-binomial distribu- tion,3437 which includes a gain factor in the Poisson distribu- tion.... In PAGE 5: ... Equivalent representations for the pdfs are also pre- sented. Some well-known density functions27 are included in Table2 for ease of comparison. The three K distributions in Table 1, K0, K, and K apos;, trans- form to three discrete distributions denoted PKO, PK, and PK apos;.... In PAGE 5: ... Properties of the negative-binomial transform are collected in Appendix A. The three A(n) distributions in Table2 are the main sub- ject of the remainder of this paper. They represent triply stochastic distributions and are obtained by smearing the mean of one distribution with another distribution whose mean is, in turn, smeared by a third distribution.... ..."

Cited by 4