Probability Density Function

f(t) = e^{-0.5[(ln(t)-µ)/s]²} / (stÖ2p)

Cumulative Density Function

F(t) = (1/[sÖ(2p)]) ò₀^t (1/x) e^{-0.5[(ln(x)-µ)/s]²}dx

Instantaneous Failure Rate

l(t) = f(t)/(1-F(t))

Median

t = t_50% = e^µ

Mean

t = e^(µ+s²/2)

Mode

t = e^(µ-s²)

Location Parameter

e^µ

Shape Parameter s

s - s,estimate of s, may be calculated as ln(t_50%/t_16%)

Probability Density Function

f(t) = ([b(t-g)^b-1]/[a^b]) (e^{-[(t-g)/a]^b})

Cumulative Density Function

F(t) = 1 - e^{-[(t-g)/a]^b}

Instantaneous Failure Rate

l(t) = [b(t-g)^b-1]/[a^b]

Location Parameter

a = t at 63.2% failure

Shape Parameter

b

Time Delay Parameter

g, not used unless data do not fit the distribution without time delay