Talk:Lomax distribution

Definition

I think there should be a definition section in the beginning of the article. Apparently Lomax originally proposed two different distributions. It might also be helpful to mention that the survival function can be expressed as $\left(1+{\frac {x}{\lambda }}\right)^{-\alpha }$ [1] or as ${\frac {\lambda ^{\alpha }}{(x+\lambda )^{\alpha }}}$ [2]. Isheden (talk) 11:02, 19 October 2012 (UTC)

It also needs to be clarified whether the support includes or excludes zero. Isheden (talk) 12:49, 19 October 2012 (UTC)

Lomax = Pareto Type II ? or Type I ?

The article says: "The Lomax distribution, also called the Pareto Type II distribution, . . . ". Using the given internal link, it is seen that the Lomax distribution is identical to the Pareto Type II distribution only when μ=0. Hence it is a simplified Pareto Type II distribution. Should this not be mentioned here?

I suppose the question is rather whether both definitions of Pareto Type II, with and without location parameter, are in common use in the literature or if the one with μ=0 is standard. Isheden (talk) 13:50, 19 October 2012 (UTC)

Be aware that μ in this context is not the same as the more common use of μ as (population) mean or expected value. Asitgoes (talk) 12:37, 19 October 2012 (UTC)

Regarding the second point: The confusion probably arises because in the normal distribution, the mean is equal to the location parameter μ. Isheden (talk) 12:46, 19 October 2012 (UTC)

And in the Logistic distribution and many more. Asitgoes (talk) 13:16, 19 October 2012 (UTC)

Some more. In the section "Relation to the Pareto distribution" it is said that: "The Lomax distribution is a Pareto Type I distribution shifted so that its support begins at zero." There is quite some difference between Type I and Type II so that this statement needs explanation. Could someone give that? Asitgoes (talk)13:05, 19 October 2012 (UTC)