represents the Hjorth distribution with location parameter m, scale parameter s, and shape parameter f.
- HjorthDistribution is a distribution that has been applied in reliability analysis for modeling different classes of failure behavior.
- The survival function for value in a Hjorth distribution is given by for and otherwise.
- HjorthDistribution[m,s,f] allows m and s to be any real positive numbers and f to be any non-negative real number.
- HjorthDistribution[m,s,f] allows m, s and f to be any quantities such that m*s and m*f are dimensionless. »
- HjorthDistribution can be used with such functions as Mean, CDF, and RandomVariate.
Examplesopen allclose all
Basic Examples (3)
The lifetime of a device follows HjorthDistribution. Find the reliability of the device:
The failure behavior of a component is described by HjorthDistribution with parameters , and . Find the probability that the component fails within its first year:
A piece of electronic equipment has initially high failure rate due to the randomness in the quality variations during its production. Its lifetime can be modeled by HjorthDistribution with parameters , and . Plot the hazard function:
To avoid early failures, the equipment is operated at stress level during a "burn-in" period. Find the length of the burn-in period after which the failure probability within the first year is reduced by half:
Find the estimated distribution for both components, assuming HjorthDistribution:
A simple mechanical system is composed of three independent components: two of type A and one of type B. The system works as long as one component of each type is working. The failure times of each component type follow the distributions:
Properties & Relations (5)
Hjorth distribution simplifies to RayleighDistribution:
ExponentialDistribution is a limiting case of Hjorth distribution:
Possible Issues (5)
HjorthDistribution is not defined when m or s is not a positive real number:
HjorthDistribution is not defined when f is a non-negative real number:
Wolfram Research (2017), HjorthDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/HjorthDistribution.html.
Wolfram Language. 2017. "HjorthDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HjorthDistribution.html.
Wolfram Language. (2017). HjorthDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HjorthDistribution.html