Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/S_Integral_Theorem.R

Given n Bernoulli experiments with success probability p, this function calculates and plots the exact probability and the approximate probability that a successful event occurs between linf+i (0<=i<=lsup-linf-1) and lsup times. It also calculates the difference between these probabilities and shows all the computations in a table.

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`n` |
An integer vector with the numbers of repetitions of the Bernoulli experiment. |

`p` |
A real value with the probability that a successful event will happen in any single Bernoulli experiment (called the probability of success). |

`linf` |
An integer vector, of the same length than n, with the minimum numbers of times that the successful event should happen. |

`lsup` |
An integer vector, of the same length than n, with the maximum numbers of times that the successful event should happen. |

`Compare` |
A logical value, if TRUE the function calculates both the exact probability and the approximate probability that a successful event occurs and compares these probabilities. |

`Table` |
A logical value, if TRUE the function shows a table with the carried out computations. |

`Graph` |
A logical value, if TRUE the function plots both the exact probability and the approximate probability that a successful event occurs. |

`GraphE` |
A logical value, if TRUE the function shows the graphic of the errors in the approximation. |

Bernoulli experiments are sequences of events, in which successive experiments are independent and at each experiment the probability of appearance of a "successful" event (p) remains constant. It is necessary that linf < lsup.

A graph and/or a table.

Department of Mathematics. University of Oriente. Cuba.

Larisa Zamora and Jorge Diaz

Gnedenko, B. V. (1978). The Theory of Probability. Mir Publishers. Moscow.

Integral_Theorem, Local_Theorem.

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S_Integral_Theorem (n = 200, p = 0.5, linf = 0, lsup = 100, Compare = TRUE, Table = TRUE,
Graph = TRUE, GraphE = TRUE)
## The function is currently defined as
function (n = 200, p = 0.5, linf = 0, lsup = 100, Compare = TRUE,
Table = TRUE, Graph = TRUE, GraphE = TRUE)
{ Integral_Theorem <- function(n = 100, p = 0.5, linf = 0,
lsup = 50) {
A <- (linf - n * p)/sqrt(n * p * (1 - p))
B <- (lsup - n * p)/sqrt(n * p * (1 - p))
P <- pnorm(B) - pnorm(A)
return(P)
}
layout(matrix(1))
PNormal <- numeric()
Dif <- numeric()
PBin <- numeric()
k <- lsup - linf - 1
PNormal[1] <- Integral_Theorem(n, p, linf, lsup)
PBin[1] <- 0
for (j in linf:lsup) PBin[1] <- PBin[1] + dbinom(j, n, p)
Dif[1] <- abs(PBin[1] - PNormal[1])
for (i in 1:k) {
linf_i <- linf + i
PNormal[i + 1] <- Integral_Theorem(n, p, linf_i, lsup)
if (Compare == TRUE) {
PBin[i + 1] <- 0
for (j in linf_i:lsup) PBin[i + 1] <- PBin[i + 1] +
dbinom(j, n, p)
Dif[i + 1] <- abs(PBin[i + 1] - PNormal[i + 1])
}
}
if (Graph == TRUE & GraphE == TRUE) {
layout(matrix(c(1, 1, 2, 2), 2, 2, byrow = TRUE))
}
if (Graph == TRUE) {
ymini <- min(PNormal[k + 1], PBin[k + 1]) - 0.05
ymaxi <- max(PNormal[1], PBin[1]) + 0.05
mfg <- c(1, 1, 2, 2)
plot(PNormal, ylim = c(ymini, ymaxi), type = "l", main = "The Integral Limit Theorem",
xlab = "k (linf<=k<=lsup)", ylab = "Probability",
col = "red")
mtext("Integral Theorem", line = -1, side = 1, adj = 1,
col = "red")
if (Compare == TRUE) {
points(PBin, type = "p", col = "blue")
mtext("Binomial Probability", line = -2, side = 1,
adj = 1, col = "blue")
}
}
if (GraphE == TRUE) {
mfg <- c(2, 1, 2, 2)
dmini <- min(Dif) - 0.01
dmaxi <- max(Dif) + 0.01
plot(Dif, ylim = c(dmini, dmaxi), type = "b", main = "Errors",
xlab = "m", ylab = "Errors", col = "green")
abline(a = 0, b = 0, col = "red")
}
if (Table == TRUE) {
Ak <- array(1:(k + 1))
if (Compare == TRUE)
TablaR <- data.frame(k = Ak, PBinomial = PBin, T_Integral = PNormal,
Difference = Dif)
else TablaR <- data.frame(K = Ak, T_Integral = PNormal)
TablaR
}
}
``` |

ExpRep documentation built on July 4, 2017, 9:45 a.m.

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