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The Hosmer–Lemeshow test is a statistical test for goodness of fit and calibration for logistic regression models. It is used frequently in risk prediction models. The test assesses whether or not the observed event rates match expected event rates in subgroups of the model population.
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
A common example of a first-hitting-time model is a ruin problem, such as Gambler's ruin. In this example, an entity (often described as a gambler or an insurance company) has an amount of money which varies randomly with time, possibly with some drift. The model considers the event that the amount of money reaches 0, representing bankruptcy.
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
1.2.1 Relationship between the likelihood and probability density functions. ... As an equation: ... One example occurs in 2×2 tables, ...
The density estimates are kernel density estimates using a Gaussian kernel. That is, a Gaussian density function is placed at each data point, and the sum of the density functions is computed over the range of the data. From the density of "glu" conditional on diabetes, we can obtain the probability of diabetes conditional on "glu" via Bayes ...
The density function may be a density with respect to counting measure, i.e. a probability mass function. Two likelihood functions are equivalent if one is a scalar multiple of the other. [ a ] The likelihood principle is this: All information from the data that is relevant to inferences about the value of the model parameters is in the ...
A random variable follows a hyperbolic secant distribution if its probability density function can be related to the following standard form of density function by a location and shift transformation: = , where "sech" denotes the hyperbolic secant function.