exponential distribution (when k=1)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:organization
gptkbp:characteristic	λ/(λ-ix)
gptkbp:conjugate_prior_for	Poisson rate parameter
gptkbp:cumulativeDistributionFunction	F(x;λ) = 1 - e^{-λx} for x ≥ 0
gptkbp:entropy	1 - ln(λ)
gptkbp:hasSpecialCase	gptkb:gamma_distribution
gptkbp:hazard_function	λ
https://www.w3.org/2000/01/rdf-schema#label	exponential distribution (when k=1)
gptkbp:kurtosis_(excess)	6
gptkbp:maximum_likelihood_estimator_for_λ	1/mean of sample
gptkbp:meaning	1/λ
gptkbp:medium	(ln 2)/λ
gptkbp:memoryless_property	true
gptkbp:minimum_of_independent_exponentials	gptkb:exponential_distribution_(with_sum_of_rates)
gptkbp:mode	0
gptkbp:moment_generating_function	λ/(λ-t) for t < λ
gptkbp:parameter	rate parameter (λ)
gptkbp:probability_density_function	f(x;λ) = λe^{-λx} for x ≥ 0
gptkbp:relatedTo	gptkb:Weibull_distribution_(with_shape_parameter_1) gptkb:chi-squared_distribution_(with_2_degrees_of_freedom) Rayleigh distribution (as a special case)
gptkbp:skewness	2
gptkbp:sum_of_n_independent_exponentials	gptkb:gamma_distribution_(with_shape_n)
gptkbp:supports	x ≥ 0
gptkbp:used_in	queueing theory survival analysis reliability engineering
gptkbp:usedFor	modeling time between events in a Poisson process
gptkbp:variant	1/λ^2
gptkbp:bfsParent	gptkb:Weibull_distribution gptkb:Erlang_distribution
gptkbp:bfsLayer	7