In[]:=
kiesDistribution[λ_,α_]:=ProbabilityDistributionExp-λ,{x,0,1},Assumptions->{λ>0,α>0}
αλ
2
(x-1)
α-1
x
x-1
α
x
x-1
In[]:=
l=PDF[kiesDistribution[λ,α],x]
Out[]=
|
IntegrateExp-λ,{x,0,t}(*iamunabletocomutetheCDF*)
αλ
2
(x-1)
α-1
x
x-1
α
x
x-1
Out[]=
t
∫
0
-λ
α
x
-1+x
-1+α
x
-1+x
2
(-1+x)
(*TheCDFofthekiesdistributionaspertheresearchis1-*)
-λ
α
x
-1+x
In[]:=
InverseFunction1-Exp-λ&
α
#
#-1
Out[]=
1
α
-
Log[1-#1]
λ
-1+
1
α
-
Log[1-#1]
λ
In[]:=
inv[x_]=;
1
2
-
Log[1-x]
2
-1+
1
2
-
Log[1-x]
2
In[]:=
data=RandomVariate[UniformDistribution[{0,1}],100];
In[]:=
data1=Map[inv,data];
(*ineedtofindtheestimatesw.r.tdata1*)
In[]:=
FindDistributionParameters[data,testDistribution[λ,α],ParameterEstimator->"MaximumLikelihood"]
Out[]=
{α2.75467,λ834.196}
In[]:=
params=FindDistributionParameters[data1,kiesDistribution[λ,α],ParameterEstimator->"MaximumLikelihood"]
-1+α
x.
-1+x.
-λ
α
x.
Plus[2]
2
(-1+x.)
Out[]=
FindDistributionParameters{-9.01237,-5.61173,-8.89657,-0.801259,-0.96644,-3.77114,-3.79938,-0.0715341,-2.31575,-1.36503,-6.77618,7.23394,10.6516,-0.7462,-0.221753,-0.894629,-1.43948,-0.0712283,-0.0804628,-6.83062,-0.223915,-1.16813,-0.438455,-1.41062,38.7475,-34.2576,-1.37617,-10.7725,-3.2937,-0.229302,-9.5511,-0.778716,-0.928549,-0.996912,-0.559141,6.07136,9.9237,-4.05923,2.5277,6.81934,-0.600828,4.76711,6.2914,-2.19484,-0.921761,4.3274,-2.16605,-1.52765,-0.390067,-1.97267,-1.20561,-1.75513,2.72541,-0.764134,-0.263925,-0.412119,-260.375,-4.59162,-3.66996,-3.22301,-3.19767,3.5258,-1.80497,-0.334725,2.64362,-0.672936,-0.840844,-0.652154,-2.72205,-2.88993,-0.365252,-3.60783,-6.42154,-0.645985,8.38598,-2.45132,-0.460941,-1.74374,-7.40333,-0.210942,-0.557714,-7.82489,-2.07933,-1.20883,3.82705,-725.352,-7.6685,4.63555,-0.428798,-0.541144,-1.0464,-0.191818,-0.968265,-1.07028,-0.121647,-2.30747,-2.65331,-6.78997,-1.77624,-0.363254},ProbabilityDistributionαλ,x.,0,1,Assumptions{λ>0,α>0},ParameterEstimatorMaximumLikelihood
-1+α
x.
-1+x.
-λ
α
x.
-1+x.
2
-1+x.
In[]:=
Plot[l,{x,0,1}]
Out[]=