Distribution  class=CompositeDistribution name=CompositeDistribution function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[x,y0] evaluationImplementation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[x] outputVariablesNames=[y0] formulas=[x^2 + 2 * sin(x)] gradientImplementation=class=SymbolicGradient name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[x] outputVariablesNames=[y0] formulas=[x^2 + 2 * sin(x)] hessianImplementation=class=SymbolicHessian name=Unnamed evaluation=class=SymbolicEvaluation name=Unnamed inputVariablesNames=[x] outputVariablesNames=[y0] formulas=[x^2 + 2 * sin(x)] antecedent=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1] bounds=class=Point name=Unnamed dimension=3 values=[-7.65063,-0.739085,7.65063] values=class=Point name=Unnamed dimension=3 values=[56.5733,-0.800977,60.4909] probabilities=class=Point name=Unnamed dimension=3 values=[1e-14,0.229928,1] increasing=[0,1]
Distribution  CompositeDistribution=f(Normal(mu = 0, sigma = 1)) with f=[x]->[x^2 + 2 * sin(x)]
Elliptical =  False
Continuous =  True
oneRealization= [1.51269]
oneSample first= [-0.304726]  last= [4.32165]
mean= [0.981731]
covariance= [[ 3.68811 ]]
Kolmogorov test for the generator, sample size= 100  is accepted
Kolmogorov test for the generator, sample size= 1000  is accepted
Point=  [1]
ddf     = [-0.0620066]
log pdf= -1.82876523119
pdf     = 0.1606117638
pdf (FD)= 0.1606117638
cdf= 0.621614338562
ccdf= 0.378385661438
survival= 0.378385661438
quantile= [4.91251]
cdf(quantile)= 0.95
quantile (tail)= [-0.78963]
cdf (tail)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=1 values=[-0.78963]
Survival(inverseSurvival)=0.950000
Minimum volume interval= [-0.800977, 4.91251]
threshold= [0.95]
Minimum volume level set= {x | f(x) <= 3.43805} with f=
MinimumVolumeLevelSetEvaluation(CompositeDistribution=f(Normal(mu = 0, sigma = 1)) with f=[x]->[x^2 + 2 * sin(x)])
beta= [0.0321272]
Bilateral confidence interval= [-0.79814, 5.94149]
beta= [0.95]
Unilateral confidence interval (lower tail)= [-0.800977, 4.91251]
beta= [0.95]
Unilateral confidence interval (upper tail)= [-0.78963, 60.4909]
beta= [0.95]
characteristic function=(0.421744+0.00166811j)
log characteristic function=(-0.863349+0.00395524j)
pdf gradient     = [0.0164482,-0.0648158]
cdf gradient     = [-0.274716,-0.309724]
mean= [1]
standard deviation= [1.93115]
skewness= [1.56182]
kurtosis= [6.15981]
covariance= [[ 3.72933 ]]
correlation= [[ 1 ]]
spearman= [[ 1 ]]
kendall= [[ 1 ]]
parameters= [[mean_0 : 0, standard_deviation_0 : 1]]
standard moment n= 0 , value= [1]
standard moment n= 1 , value= [1]
standard moment n= 2 , value= [4.72933]
standard moment n= 3 , value= [23.436]
standard moment n= 4 , value= [154.038]
standard moment n= 5 , value= [1261.42]
Standard representative= CompositeDistribution=f(Normal(mu = 0, sigma = 1)) with f=[x]->[x^2 + 2 * sin(x)]
antecedent= Normal(mu = 0, sigma = 1)
function= [x]->[x^2 + 2 * sin(x)]
newDistribution= CompositeDistribution=f(Normal(mu = 0, sigma = 1)) with f=[x]->[x^2 + 2 * sin(x)]
