Univariate Discrete Distributions

By J. Davis. 2006

1,329 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Water Science and Technology

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Citations in the corpus

A Comprehensive Comparison of Multiparty Secure Additions with Differential Privacy (2015, methodology): “4 (PÓLYA DISTRIBUTION [34]) Let X be a random variable following the discrete P ólya(r, p) distribution with parameters r ∈ R and p ∈ (0, 1).”
Convergence properties of the q-deformed binomial distribution (2010, neutral): “For properties of this distribution we refer to [7], Kemp [8, 9, 11] and Charalambides and Papadatos [1].”
On the Failure of the Bootstrap for Matching Estimators (2006, background): “The Mth moment of Ki given W and X0 is (Johnson, Kotz, and Kemp, 1993): E[KMi |X0,Wi = 0] = M∑ j=0 S(M, j)N0”
Content-based recommendations with Poisson factorization (2014, methodology): “For the auxiliary Poisson variables, observe that z dv is a K -dimensional latent vector of Poisson counts, which when conditioned on their observed sum w dv , is distributed as a multinomial [14, 4].”
On the Depth and Dynamics of Online Search Behavior (2004, positive): “Working backwards through this recursive relationship, we can obtain the logarithmic distribution (Johnson et al. 1993). i x ii ii x θa xX i == ]Pr[ xi = 1, 2, …, (2) where ai = -[ln(1-θi)]-1 and 0<θi<1.”
Quake: quality-aware detection and correction of sequencing errors (2010, background): “We found that k-mer copy number in various genomes has a “heavy tail” (meaning the tail of the distribution is not exponentially bounded) that is approximated well by the Zeta distribution [47], which has a single shape parameter.”
Generalized Poisson–Lindley Distribution (2010, background): “For more details, see Johnson et al. (2005). Figure 1 shows the density function of GPL distribution for selected values of and .”
Infinitely Divisible Distributions in Integer‐Valued Garch Models (2015, positive): “We are in presence of a wide class of discrete distributions which includes several well-known examples in literature such as the logarithmic and Borel laws (Johnson et al., 2005).”
Classes of Discrete Lifetime Distributions (2004, background): “IFR/DFR In Johnson et al. (1992) it was stated without proof that the negative binomial distribution with pgf ð1 qÞk=ð1 qsÞk has a decreasing hazard rate for k < 1 (DFR) and has an increasing hazard rate for k > 1 (IFR), because the probabilities are logconvex (pxpxþ2=p2xþ1 > 1) for k < 1 and…”
An empirical model for underdispersed count data (2004, methodology): “Frequently data are overdispersed, with the variance greater than the mean, and there is then a rich variety of alternative distributions that can be used to model the data (see, for example, Johnson et al., 1992, Chapters 8 and 9).”
A Balls-and-Bins Model of Trade (2014, positive): “Note that the universe of interest is the set of exporting rms, because the empirical facts are usually reported only for rms that have some exports.(23) This way we can use the balls-and-bins model to understand these moments despite the split between exporters and non-exporters being very di erent”
Generalized Additive Models for Location Scale and Shape (GAMLSS) in R (2007, background): “Johnson, Kotz, and Balakrishnan (1994, 1995); Johnson, Kotz, and Kemp (2005) are the classical reference books for most of the distributions in Tables 1 and 2.”
Regression Analysis of Multivariate Fractional Data (2016, methodology): “(see Johnson et al., 2005, Ch. 6); see inter alia Heckman and Willis (1977) and Santos Silva and Murteira (2009) for examples of the use of the betabinomial model in a regression context.”
New Results Concerning Probability Distributions with Increasing Generalized Failure Rates (2012, neutral): “A large number of well-known discrete distributions, including the Binomial, Negative Binomial, Geometric, and the Poisson distributions, satisfy δ = 1; see also Johnson et al. (2005).”
Univariate Distribution Relationships (2008, background): “…Hjorth (1980) • inverse Gaussian distribution: Chhikara and Folks (1989), Seshadri (1993) • inverted gamma distribution: Casella and Berger (2002) • logarithm distribution: Johnson, Kemp, and Kotz (2005) • logistic–exponential distribution: Lan and Leemis (2007) • Makeham distribution: Jordan…”
Discrete dispersion models and their Tweedie asymptotics (2014, methodology): “To obtain a discrete analogue of (2.1), we consider the factorial cumulant generating function (FCGF) for X (Johnson et al. , 2005, p. 55), defined by C(t) = C(t”