Setting a new pdf Distribution and estimating its parameters by MLE

 Setting a new pdf Distribution and estimating its parameters by MLE

Good morning. I need to create a pdf and esteimate its parameters by MLE method. The distribution is a power law ($ f(x)=C(k)\;x^{-k}$ ) and I need to estimate the $ k$ parameter and $ C(k)$ is determinated by the normalization condition $ \int_a^b\;C(k)\;x^{-k}=1$ . I have tried to define the power distribution with ProbabilityDistribution function usin, for example, C=5, but when I want to plot it, Mathematica doesn’t display the plot. What I’ve been writing is

distr=ProbabilityDistribution[5/x^1.05,{x,0,Infinity}]
PDF[distr,x]
Plot[%,{x,0,1}]

NOTE: when I try to define de distribution function I’m setting $ k=1.05$ , just for knowing if I’m doing it well.

Could you help me, please?

Thanks for your answers.

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