HazardFunction

Obtain exact numeric results:

Obtain a machine-precision result:

Obtain a result at any precision for a continuous distribution:

Obtain a result at any precision for a discrete distribution with inexact parameters:

Hazard function for a multivariate distribution:

Obtain a symbolic expression for the hazard function:

Hazard function for nonparametric distributions:

Compare with the value for the underlying parametric distribution:

Plot the survival function for a histogram distribution:

Plot of the survival function of a bivariate smooth kernel distribution:

Product of independent distributions:

Component mixture distribution:

Quadratic transformation of a discrete distribution:

Truncated distribution:

A copula distribution:

Formula distributions defined by its PDF:

Defined by its CDF:

Defined by its survival function:

Marginal distribution:

Find the mortality rate for lifetime distributions including exponential distribution:

Gompertz distribution:

Study the hazard function for a family of Weibull distributions:

With , used is better than new:

With , used is as good as new:

With , used is worse than new:

A casino offers you a game where you pay amount to participate and then choose a stake amount . A positive continuous random variable following a known distribution is then generated. If you collect the stake; otherwise you lose. Find the value that maximizes the profit:

Find the equation for the maximum of the expected gain:

Assuming WeibullDistribution, find the optimal stake size:

Compute the hazard function using the definition as conditional probability:

The hazard function is a ratio of the PDF and the survival function :

Symbolic closed forms do not exist for some distributions:

Numerical evaluation works:

Substitution of invalid values into symbolic outputs gives results that are not meaningful:

Passing it as an argument, it stays unevaluated: