The CDF of the Weibull distribution is
CDF(x) = 1 − exp[−(x / λ)^k]
The CCDF and my approach:
CCDF(x) = 1 - CDF(x)
CCDF(x) = 1 - (1 − exp[−(x / λ)^k])
CCDF(x) = exp[−(x / λ)^k]
Assuming the following value of scale/k and taking the natural log, ln:
k = 1,
ln(CCDF) = ln(exp[−(x / λ)^k])
ln(CCDF) = -xλ
Which yields a straight line with slope -λ.
Code:
x3 = np.linspace(1,15, 1000)
weibull_cdf = scipy.stats.weibull_min.cdf(x3, c = 1, scale = 1)
weibull_ccdf = (1 - weibull_cdf)
weibull_ccdf = np.log(weibull_ccdf)
Is this implementation solid? Would changing the scale so that scale/k = 2 change the implementation?