Search results
Results from the WOW.Com Content Network
Binomial regression models are essentially the same as binary choice models, one type of discrete choice model: the primary difference is in the theoretical motivation (see comparison). In machine learning , binomial regression is considered a special case of probabilistic classification , and thus a generalization of binary classification .
Some distributions have been specially named as compounds: beta-binomial distribution, Beta negative binomial distribution, gamma-normal distribution. Examples: If X is a Binomial(n,p) random variable, and parameter p is a random variable with beta(α, β) distribution, then X is distributed as a Beta-Binomial(α,β,n).
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution , not a binomial one.
In the case when the 3 parameters , and are positive integers, the Beta negative binomial can also be motivated by an urn model - or more specifically a basic Pólya urn model. Consider an urn initially containing α {\displaystyle \alpha } red balls (the stopping color) and β {\displaystyle \beta } blue balls.
Under BDT, using a binomial lattice, one calibrates the model parameters to fit both the current term structure of interest rates (yield curve), and the volatility structure for interest rate caps (usually as implied by the Black-76-prices for each component caplet); see aside.
A binomial test is a statistical hypothesis test used to determine whether the proportion of successes in a sample differs from an expected proportion in a binomial distribution. It is useful for situations when there are two possible outcomes (e.g., success/failure, yes/no, heads/tails), i.e., where repeated experiments produce binary data .
If follows binomial distribution with certain mean, has the conjugate beta distribution, and canonical logit link is used, then we call the model Beta conjugate model. Moreover, the mixed linear model is the normal conjugate hierarchical generalized linear models. [2]
In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options.Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting, which in general does not exist for the BOPM.