basicInci <-
function(data, k){
data <- as.numeric(data)
t <- data[1]
dat <- data[-1]
x <- dat[which(dat != 0)]
Q <- function(i, data){length(data[which(data == i)])}
D <- length(x)
D_infreq <- length(x[which(x <= k)])
if (Q(1, x) > 0 & Q(2, x) > 0){
A <- 2*Q(2, x)/((t-1)*Q(1, x) + 2*Q(2, x))
} else if (Q(1, x) > 0 & Q(2, x) == 0){
A <- 2/((t-1)*(Q(1, x) - 1) + 2)
} else {
A <- 1
}
C_infreq <- 1 - Q(1, x)/sum(x[which(x <= k)])*(1-A)
j <- c(1:k)
b1 <- sum(sapply(j, function(j)j*(j-1)*Q(j, x)))
b2 <- sum(sapply(j, function(j)j*Q(j, x)))
gamma_infreq_square <- max(D_infreq/C_infreq*t/(t - 1)*b1/b2/(b2) - 1, 0)
CV_infreq <- sqrt(gamma_infreq_square)
D_freq <- length(x[which(x > k)])
BASIC.DATA <- matrix(paste(c("D", "t", "k", "D_infreq", "C_infreq", "CV_infreq", "D_freq"),
c(D,t,k,D_infreq,C_infreq,CV_infreq,D_freq),
sep = "="), ncol=1)
colnames(BASIC.DATA)=c("Value")
rownames(BASIC.DATA)=c("Number of observed species","Number of sample/quadrats","Cut-off point",
"Number of observed species for infrequent species","Estimated sample coverage for infrequent species",
"Estimated CV for infrequent species",
"Number of observed species for frequent species")
return(list(BASIC.DATA, D, t, D_infreq, C_infreq, CV_infreq, D_freq))
}
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