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c = 2;
P = N[n*Log[n]]
K = N[c*Log[n]]

Needs["PlotLegends`"];

PrDEqK[P_, K_, n_, c_, k_] := Module[{p, q, r, ps, qs, m, tmp},
    r = Sqrt[(c*Log[n])/(n*\[Pi])];
    p = \[Pi]*r^2;
    q = 1 - p;
    ps = 1 - Binomial[P - K, K]/Binomial[P, K];
    qs = 1 - ps;

   N[Sum[Binomial[n - 1, m]*p^m*q^(n - 1 - m)*Binomial[m, k]*ps^k*
      qs^(m - k), {m, k, n - 1}]]

   ];
Plot[CDF[{PrDEqK[P, K, 20, c, k], {k, 1, 8},Filling -> Axis
]

i'm not getting the CDF plot...what is the problem?

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1
  • $\begingroup$ CDF, for one thing, is for distributions, you are trying to plot a function. There are other issues with the code, please attempt to fix these and add some context to the question. $\endgroup$
    – ciao
    Jan 17, 2014 at 8:39

2 Answers 2

1
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As has been CDF acts on distribution objects. You have defined a discrete PMF. With all due respect the plot by Boson is not a CDF but a continous plot of PMF.

Reproduing user-defined:

c = 2;
n = 20;
P = N[n*Log[n]];
K = N[c*Log[n]];

PrDEqK[P_, K_, n_, c_, k_] := 
  Module[{p, q, r, ps, qs, m, tmp}, r = Sqrt[(c*Log[n])/(n*\[Pi])];
   p = \[Pi]*r^2;
   q = 1 - p;
   ps = 1 - Binomial[P - K, K]/Binomial[P, K];
   qs = 1 - ps;
   N[Sum[Binomial[n - 1, m]*p^m*q^(n - 1 - m)*Binomial[m, k]*ps^k*
      qs^(m - k), {m, k, n - 1}]]];

To generate CDF:

cdf[k_] := Sum[PrDEqK[P, K, 20, c, j], {j, 0, k}];

Visualizing:

DiscretePlot[cdf[k], {k, 0, 8}]

enter image description here

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3
  • $\begingroup$ can we plot this CDF combinedly for different values of 'n'that i fixed to 20.. $\endgroup$
    – user11609
    Jan 17, 2014 at 11:13
  • $\begingroup$ @user11609 yes. Just redefine function to:cdfgeneral[n_,k_]:=Sum[PrDEqK[P, K, n, c, j], {j, 0, k}]; $\endgroup$
    – ubpdqn
    Jan 17, 2014 at 11:16
  • $\begingroup$ okk...thank u so much.. $\endgroup$
    – user11609
    Jan 17, 2014 at 11:20
1
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I tried to clean your code a little and it worked right away:

c = 2;
n = 20;
P = N[n*Log[n]];
K = N[c*Log[n]];

PrDEqK[P_, K_, n_, c_, k_] := 
  Module[{p, q, r, ps, qs, m, tmp}, r = Sqrt[(c*Log[n])/(n*\[Pi])];
   p = \[Pi]*r^2;
   q = 1 - p;
   ps = 1 - Binomial[P - K, K]/Binomial[P, K];
   qs = 1 - ps;
   N[Sum[Binomial[n - 1, m]*p^m*q^(n - 1 - m)*Binomial[m, k]*ps^k*
      qs^(m - k), {m, k, n - 1}]]];

Plot[PrDEqK[P, K, n, c, k], {k, 1, 8}, Filling -> Axis]

enter image description here

EDIT: I am sorry, I have not read the question thoroughly and did not notice you wanted a CDF. ubpdqn is absolutly right.

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