dtrgg(TRIANGG)
dtrgg()所属R语言包：TRIANGG
General discrete triangular distributions
一般离散三角分布
译者：生物统计家园网 机器人LoveR
描述----------Description----------
The function plots general discrete triangular distributions
一般的函数曲线离散三角分布
用法----------Usage----------
dtrgg(m,a1,a2,h1,h2,y)
参数----------Arguments----------
参数：m
The mode $m$ is an integer
百万元百万元模式是一个整数，
参数：a1, a2
The left arm $a_1$ and right arm $a_2$ are non-negative integers
左臂$ A_1 $，右臂$ A_2 $均为非负整数
参数：h1, h2
The left order $h_1$ and right order $h_2$ are positive real numbers
左的顺序H_1 $和正确的顺序H_2 $是正实数
参数：y
The vector of entire observations
整个观测向量
Details
详细信息----------Details----------
The general discrete triangular distribution has the probability mass function
一般的离散三角分布的概率密度函数
$ Pr(Y=y) = (1/D)[1-{(m-y)/(a_1+1)}^h_1]1_{m-a_1,...,m-2,m-1}(y)$
$镨（Y = y）的=（1 / D）[1 - {（我的）/（A_1 1）} ^ H_1] 1_ {间A_1，...，米-2，m-1的}（Ŷ ）
$+ (1/D)[1-{(y-m)/(a_2+1)}^h_2]1_{m,m+1,...,m+a_2}(y) $
$ +（1 / D）[1 - {（YM）/（A_2 1）} ^ H_2] 1_ {M，M +1，...，且m + A_2}（y）的$
with the normalizing constant $D=(a_1+a_2+1) - (a_1+1)^-h_1sum_k=1^a_1k^h_1 - (a_2+1)^-h_2sum_k=1^a_2k^h_2$.
用归一化常数$ D =（A_1 + A_2 1） - （A_1 1）^-h_1sum_k = 1 ^ a_1k ^ H_1 - （A_2 1）^-h_2sum_k = 1 ^ a_2k ^ H_2 $。
值----------Value----------
The function returns the probability mass function in [0,1] of the corresponding $y$ value.
该函数返回概率密度函数在[0,1]的相应价值$ Y $。
（作者）----------Author(s)----------
Tristan Senga Kiess\'e, Francial G. Libengu\'e, Silvio S. Zocchi, C\'elestin C. Kokonendji
参考文献----------References----------
Kokonendji, C.C. and Zocchi, S.S. (2010). Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions. Statistics and Probability Letters, 80, 1655–1662.
Kokonendji, C.C., Senga Kiess\'e, T. and Zocchi, S.S. (2007). Discrete triangular distributions and non-parametric estimation for probability mass function. Journal of Nonparametric Statistics, 19, 241–254.
参见----------See Also----------
'dtrg' for symmetric discrete triangular distributions
“dtrg”对称离散三角分布
实例----------Examples----------
#The following example illustrates different shapes of general[下面的例子说明不同形状的一般]
#discrete triangular distributions : [离散三角分布：]
y=-3:15
ym2_10=y
m=2
h1=1/2
h2=1/3
a1=4
a2=12
Tm2=dtrgg(m,a1,a2,h1,h2,y)
m=10
h1=1/2
h2=1/3
a1=12
a2=4
Tm10=dtrgg(m,a1,a2,h1,h2,y)
y=3:21
ym9_15=y
m=9
h1=1/2
h2=3
a1=5
a2=11
Tm9=dtrgg(m,a1,a2,h1,h2,y)
m=15
h1=1/2
h2=3
a1=11
a2=5
Tm15=dtrgg(m,a1,a2,h1,h2,y)
par(mfrow=c(1,2))
plot(ym2_10,Tm2,xlab="y",ylab="P(Y=y)", ylim=c(0,0.3),main="h1=1/2 and h2=1/3",pch=20,
col="grey",cex.lab=1.5,cex.axis=1.5,lwd=2)
lines(ym2_10,Tm2,lty=1,col="grey",lwd=2)
points(ym2_10,Tm10,xlab="y",ylab="P(Y=y)", main="h1=1/2 and h2=1/3",pch=20,
col="black",cex.lab=1.5,cex.axis=1.5,lwd=2)
lines(ym2_10,Tm10,lty=2,lwd=2)
op <- par(bg="white")
legend(0,0.3,c("m=2,a1=4,a2=12", "m=10,a1=12,a2=4"),
pch=c(20,20), lty=c(1,2),col=c("grey","black"),cex =1,lwd=c(2,2))
plot(ym9_15,Tm9,xlab="y",ylab="P(Y=y)",ylim=c(0,0.2), main="h1=1/2 and h2=3",pch=20,
col="grey",cex.lab=1.5,cex.axis=1.5)
lines(ym9_15,Tm9,lty=1,col="grey",lwd=2)
points(ym9_15,Tm15,xlab="y",ylab="P(Y=y)", main="h1=1/2 and h2=3",pch=20,
col="black",cex.lab=1.5,cex.axis=1.5)
lines(ym9_15,Tm15,lty=2,lwd=2)
op <- par(bg="white")
legend(5,0.2,c("m=9,a1=5,a2=11", "m=15,a1=11,a2=5"),
pch=c(20,20), lty=c(1,2),col=c("grey","black"),cex =1,lwd=c(2,2))
## The function is defined as[＃函数被定义为]
function(m,a1,a2,h1,h2,y){
T=rep(0,length(y));
if ((a1==0)&(a2==0))
{
{for (j in 1:length(y)) # Loop in j for each observation y[在j循环的每个观察Ÿ]
{if (y[j]==m)
T[j]= 1 # Dirac distribution at m [狄拉克分布在m]
else{
T[j]=0
}
}
}
}
else if ((h1==0)&(h2==0))
{
{for (j in 1:length(y))
{if (y[j]==m)
T[j]= 1 # Dirac distribution at m [狄拉克分布在m]
else{
T[j]=0
}
}
}
}
else if ((h1==Inf)&(h2==Inf))
{
{for (j in 1:length(y))
{if (y[j]>=(m-a1) & y[j]<=(m+a2) & y[j]==as.integer(y[j]))
# Support {m-a1,...,m,...m+a2}[支持{-α1，...，米，...米+α2}]
T[j]= 1/(a1+a2+1)
# Discrete uniform distribution [离散均匀分布]
else{
T[j]=0
}
}
}
}
else if ((h1==Inf)&(h2==0))
{
{for (j in 1:length(y))
{if (y[j]>=(m-a1) & y[j]<=m & y[j]==as.integer(y[j]))
# Support {m-a1,...,m-1,m}[支持{-α1，...，m-1的，米}]
T[j]= 1/(a1+1)
# Discrete uniform distribution [离散均匀分布]
else{
T[j]=0
}
}
}
}
else if ((h1==0)&(h2==Inf))
{
{for (j in 1:length(y))
{if (y[j]>=m & y[j]<=(m+a2) & y[j]==as.integer(y[j]))
# Support {m,m+1,...,m+a2}[支持M，M +1，...，M + A2}]
T[j]= 1/(a2+1)
# Discrete uniform distribution [离散均匀分布]
else{
T[j]=0
}
}
}
}
else
{
u1=0;
u2=0;
{for (k in 1:a1)
{
u1=u1+k^h1
}
}
{for (k in 1:a2)
{
u2=u2+k^h2
}
}
D=(a1+a2+1)-(a1+1)^(-h1)*u1 -(a2+1)^(-h2)*u2 # Normalizing constant [标准化常数]
{for (j in 1:length(y))
{if (y[j]>=(m-a1) & y[j]<=(m-1)& y[j]==as.integer(y[j]))
# Support {m-a1,...,m-2,m-1}[支持{-α1，...，米2时，m-1}]
T[j]= (1 - ((m-y[j])/(a1+1))^h1)/D
# Discrete triangular distribution a1, h1[离散三角分布A1，H1]
else if (y[j]>=m & y[j]<=(m+a2)& y[j]==as.integer(y[j]))
# Support {m,m+1,...m+a2}[支持M，M +1，...，M + A2}]
T[j]= (1 - ((y[j]-m)/(a2+1))^h2)/D
# Discrete triangular distribution a2, h2[离散的三角形分布A2，H2]
else{
T[j]=0
}
}
}
}
return(T)
}
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
注3：如遇到不准确之处，请在本贴的后面进行回帖，我们会逐渐进行修订。
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发表于 2012-10-1 12:03:36
