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 Probability and Statistics Basic Probability and Statistics Math Forum

 October 30th, 2016, 10:36 PM #1 Senior Member   Joined: Feb 2014 Posts: 114 Thanks: 1 Change shape Hello, Can we change histogram shape , to consider after change shape ,area of histogram be 1 ?
 October 31st, 2016, 12:29 PM #2 Global Moderator   Joined: May 2007 Posts: 6,788 Thanks: 708 Question is too vague. Any histogram can be scaled to make the area 1, with or without changing shape. Thanks from topsquark
October 31st, 2016, 08:54 PM   #3
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Quote:
 Originally Posted by mathman Question is too vague. Any histogram can be scaled to make the area 1, with or without changing shape.

Can we transform histogram from upper figure to lower figure in picture?(Consider after transform and changed shape , still area is 1 )

 November 1st, 2016, 01:17 PM #4 Global Moderator   Joined: May 2007 Posts: 6,788 Thanks: 708 You can transform the curve in general (as long as they are not too crazy). Once you get the shape you want, then scale to get the area = 1. Thanks from topsquark
November 1st, 2016, 01:48 PM   #5
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Quote:
 Originally Posted by mathman You can transform the curve in general (as long as they are not too crazy). Once you get the shape you want, then scale to get the area = 1.
How can perform this? (It is better to be pulled to the right curve peaks.)
Could you give me an example please?

 November 2nd, 2016, 04:31 AM #6 Senior Member   Joined: Feb 2014 Posts: 114 Thanks: 1 Please help me
 November 2nd, 2016, 11:43 AM #7 Senior Member   Joined: Feb 2014 Posts: 114 Thanks: 1 In another way, i want wide kurtosis.
November 2nd, 2016, 12:14 PM   #8
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Quote:
 Originally Posted by life24 In another way, i want wide kurtosis.
Why not match a Rayleigh distribution to your original distribution and then just adjust the spread parameter $\sigma$

The location of the peak in your original distribution is the value of $\sigma$

Increasing $\sigma$ will spread the distribution out.

The Kurtosis of the Rayleigh distribution is constant though.

The Erlang distribution could be used. It has two adjustable parameters

$k \in \mathbb{N}$

$\lambda \in \mathbb{R},~\lambda > 0$

The original peak is at $\dfrac{k-1}{\lambda}$

The kurtosis is $\dfrac{6}{k}$

Increasing $k$ will move your peak to the right, spread the distribution out, and increase the kurtosis.

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