DAVIS DISTRIBUTION
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Negative binomial distributionIn probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified/constant/fixed number of successes r {\displaystyle r} occur. For example, we can define rolling a 6 on some dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ( r = 3 {\displaystyle r=3} ). In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution. An alternative formulation is to model the number of total trials (instead of the number of failures). In fact, for a specified (non-random) number of successes (r), the number of failures (n − r) is random because the number of total trials (n) is random. For example, we could use the negative binomial distribution to model the number of days n (random) a certain machine works (specified by r) before it breaks down. The negative binomial distribution has a variance μ / p {\displaystyle \mu /p} , with the distribution becoming identical to Poisson in the limit p → 1 {\displaystyle p\to 1} for a given mean μ {\displaystyle \mu } (i.e. when the failures are increasingly rare). Here p ∈ [ 0 , 1 ] {\displaystyle p\in [0,1]} is the success probability of each Bernoulli trial. This can make the distribution a useful overdispersed alternative to the Poisson distribution, for example for a robust modification of Poisson regression. In epidemiology, it has been used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. More generally, it may be appropriate where events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term. The term "negative binomial" is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability mass function of the distribution can be written more simply with negative numbers.
Multivariate normal distributionIn probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables, each of which clusters around a mean value.
Gamma distributionIn probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use: With a shape parameter α and a scale parameter θ With a shape parameter α {\displaystyle \alpha } and a rate parameter λ = 1 / θ {\displaystyle \lambda =1/\theta } In each of these forms, both parameters are positive real numbers. The distribution has important applications in various fields, including econometrics, Bayesian statistics, and life testing. In econometrics, the (α, θ) parameterization is common for modeling waiting times, such as the time until death, where it often takes the form of an Erlang distribution for integer α values. Bayesian statisticians prefer the (α,λ) parameterization, utilizing the gamma distribution as a conjugate prior for several inverse scale parameters, facilitating analytical tractability in posterior distribution computations. The probability density and cumulative distribution functions of the gamma distribution vary based on the chosen parameterization, both offering insights into the behavior of gamma-distributed random variables. The gamma distribution is integral to modeling a range of phenomena due to its flexible shape, which can capture various statistical distributions, including the exponential and chi-squared distributions under specific conditions. Its mathematical properties, such as mean, variance, skewness, and higher moments, provide a toolset for statistical analysis and inference. Practical applications of the distribution span several disciplines, underscoring its importance in theoretical and applied statistics. The gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and a 1 / x {\displaystyle 1/x} base measure) for a random variable X for which E[X] = αθ = α/λ is fixed and greater than zero, and E[ln X] = ψ(α) + ln θ = ψ(α) − ln λ is fixed (ψ is the digamma function).
Walt Disney Studios Motion PicturesWalt Disney Studios Motion Pictures is an American film distributor within the Disney Entertainment division of the Walt Disney Company. It handles theatrical and occasional digital distribution, marketing, and promotion for films produced and released by the Walt Disney Studios, including Walt Disney Pictures, Walt Disney Animation Studios, Pixar, Marvel Studios, Lucasfilm, 20th Century Studios, and Searchlight Pictures, though it operates its own autonomous theatrical distribution and marketing unit in the United States. The company was originally established by Walt Disney in 1953 as Buena Vista Film Distribution Company Inc. (later renamed Buena Vista Distribution Inc. and Buena Vista Pictures Distribution Inc.). It took on its current name in late 2007.
Davis distributionIn statistics, the Davis distributions are a family of continuous probability distributions. It is named after Harold T. Davis (1892–1974), who in 1941 proposed this distribution to model income sizes. (The Theory of Econometrics and Analysis of Economic Time Series). It is a generalization of the Planck's law of radiation from statistical physics.
Empire DistributionEmpire Distribution, Records and Publishing Inc. (stylized as EMPIRE) is an independent American record label, distribution and publishing company founded in 2010 by Ghazi Shami. Based in San Francisco, EMPIRE has offices in New York, London, Lagos, and Johannesburg in addition to recording studios in San Francisco and New York. Shami, a San Francisco native with a background in music and tech, founded Empire as a digital distribution company focused on hip hop and rap. Developing proprietary software that allowed managers and artists to easily track airplay and sales, Empire paid monthly royalties to artists, many of whom had not previously earned digital revenue, and gained early support from the Bay Area's artist community. In 2014, Shami, known as Ghazi, launched the Empire label. Empire Africa, Empire Latino, and Empire Nashville divisions were later established. Since its founding—in partnership with artists and artist labels—Empire has released music by artists including Kendrick Lamar, Anderson .Paak, Shaboozey, Fat Joe, Tyga, Asake, Fireboy DML, XXXTentacion, G-Dragon, Philthy Rich, Young Dolph, Key Glock, King Von, Tink, Black Sherif, Yung Bleu, D Smoke, T-Pain, Snoop Dogg, DRAM, Cardi B and Emtee, among others. Empire Publishing was founded in 2020.
Tina Davis (music industry executive)Tina Davis is an American music industry executive. She is the president of Empire (stylized as EMPIRE), an independent record label, distribution and publishing company. Raised in Vallejo, California, Davis was the first woman to head the A&R department at Def Jam. In 2008, she founded Phase Too, an artist management firm. Among others, she managed Chris Brown. Davis joined Empire in 2018 as vice president of A&R. She was promoted to senior vice president of A&R in 2021 and named president of the company in June 2023.
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