Group Abstract Group Abstract

Message Boards Message Boards

What value of x splits the area under the curve in half?

Jonathan Wooldridge
Posted 3 years ago

How do I calculate at what point on the x axis half the area under the curve is to the right of x, and half to the left?
POSTED BY: Jonathan Wooldridge
10 Replies
Sort By:
Hans Milton
Hans Milton
Posted 3 years ago

is there a good color pattern for emphasizing a specified region on the z-axis for tries?

Maybe you could use Mesh ?

triesPlot[nrOfTries_]:=Plot3D[
  Log[1-certainty]/Log[failure],{certainty,0,1},{failure,0.0001,1},
  PlotRange->{0,20},AxesLabel->{"risk","failure","tries"},
  ColorFunction->Function[ColorData["NeonColors"][Log[1-#1]/Log[#2]]],
  Mesh->{{nrOfTries}},MeshFunctions->{#3&},MeshStyle->{Green,Thick},
  ClippingStyle->None
]

triesPlot[10]
POSTED BY: Hans Milton
POSTED BY: Robert Nowak

So here's tries as a function of risk and failure; is there a good color pattern for emphasizing a specified region on the z-axis for tries?
POSTED BY: Jonathan Wooldridge
Hans Milton
Hans Milton
Posted 3 years ago

Two ways.
Using NSolve

f[x_] := Integrate[Log[u]/Log[0.85], {u, 0.0001, x}]
NSolve[2*f[x] == f[1] && 0 < x < 1, x]

ProbabilityDistribution with InverseCDF gives the same result

dist = ProbabilityDistribution[Log[x]/Log[0.85], {x, 0.0001, 1}, Method -> "Normalize"];
InverseCDF[dist, 1/2]
POSTED BY: Hans Milton

We could set some arbitrary limit to the approach to zero; maybe four digits of precision, so 0.0001
POSTED BY: Jonathan Wooldridge

This would not really help if the area indeed would be infinite - which is not the case.
POSTED BY: Robert Nowak

The methods below also produce the answer 0.1867, and use the technique of selecting a point arbitrarily close to zero.
POSTED BY: Jonathan Wooldridge

Nobody questioned that this works.
POSTED BY: Robert Nowak
Rohit Namjoshi
Rohit Namjoshi
Posted 3 years ago

In this example, the area under the curve is infinite. Is there some minimum value for risk?

POSTED BY: Rohit Namjoshi

This is a wrong statement.

Integrate[Log[x]/Log[17/20], {x, 0, 1}]

1/Log[20/17]
POSTED BY: Robert Nowak
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard