In
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
, the Mills ratio (or Mills's ratio
) of a
continuous random variable
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...
is the function
:
where
is the
probability density function
In probability theory, a probability density function (PDF), or density of a 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 ...
, and
:
is the
complementary cumulative distribution function (also called
survival function
The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time.
The survival function is also known as the survivor function
or reliability function.
The term ...
). The concept is named after
John P. Mills
John is a common English name and surname:
* John (given name)
* John (surname)
John may also refer to:
New Testament
Works
* Gospel of John, a title often shortened to John
* First Epistle of John, often shortened to 1 John
* Second E ...
. The Mills ratio is related to the
hazard rate
Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysi ...
''h''(''x'') which is defined as
: