| Type: | Package |
| Title: | Central Limit Theorem Experiments (Theoretical and Simulation) |
| Version: | 1.3 |
| Date: | 2016-02-18 |
| Author: | Simiao Ye, Jingning Mei |
| Maintainer: | Simiao Ye <simiao.ye@gmail.com> |
| Description: | Central limit theorem experiments presented by data frames or plots. Functions include generating theoretical sample space, corresponding probability, and simulated results as well. |
| License: | GPL-2 |
| LazyData: | true |
| NeedsCompilation: | no |
| Packaged: | 2016-02-19 02:36:42 UTC; ye |
| Repository: | CRAN |
| Date/Publication: | 2016-02-19 08:49:57 |
Histogram and Q-Q plot of simulated Beta distribution
Description
Histogram and Q-Q plot of simulated Beta distribution
Usage
beta.simu.plot(n, shape1, shape2, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of trials in one simulation |
shape1 |
non-negative parameters of the Beta distribution |
shape2 |
non-negative parameters of the Beta distribution |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Beta distribution, red curve represents theoretical density
Examples
beta.simu.plot(n = 5, shape1 = 3, shape2 = 1, times = 100)
Histogram and Q-Q plot of simulated Binomial distribution
Description
Histogram and Q-Q plot of simulated Binomial distribution
Usage
binom.simu.plot(n, size, prob, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of observations |
size |
number of trials (zero or more) |
prob |
probability of success on each trial |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Binomial distribution, red curve represents theoretical density
Examples
binom.simu.plot(n = 10, size = 5, prob = 0.2, times = 100)
Histogram and Q-Q plot of simulated Chi-Squared distribution
Description
Histogram and Q-Q plot of simulated Chi-Squared distribution
Usage
chisq.simu.plot(n, df, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of trials in one simulation |
df |
degrees of freedom (non-negative, but can be non-integer) |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Chi-Squared distribution, red curve represents theoretical density
Examples
chisq.simu.plot(n = 5, df = 4, times = 100)
Theoretical Probability Distribution of Flipping Coins
Description
Mean and probability of flipping fair or loaded coin
Usage
coin(n, prob = NULL)
Arguments
n |
number of trials |
prob |
probability assigned to each possible outcome |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Mean value and corresponding probabilities for all possible outcomes.
Examples
coin(n = 4)
coin(6, c(0.1, 0.9))
Theoretical Probability Distribution Plot of Flipping Coins
Description
Probability plot of flipping fair or loaded coin
Usage
coin.plot(n, prob = NULL, col = "black", type = NULL,
main = NULL, sub = NULL)
Arguments
n |
number of trials |
prob |
probability assigned to each possible outcome |
col |
color of the plot |
type |
type of plot |
main |
an overall title for the plot |
sub |
a sub title for the plot |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Plot of mean value and corresponding probabilities for all possible outcomes.
Examples
coin.plot(n = 4, col ='red', type = 'p')
coin.plot(3, prob = c(0.3, 0.7))
Probability Distribution of Simulated Coins Flipping
Description
Mean and probability plot of flipping fair or loaded coin
Usage
coin.simu(n, times, prob = NULL)
Arguments
n |
number of trials in one simulation |
times |
number of simulations |
prob |
probability assigned to each possible outcome |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Mean value and corresponding probabilities for all simulated outcomes.
Examples
coin.simu(n = 4, times = 1000)
coin.simu(4, 1000, prob = c(0.3, 0.7))
Probability Distribution Plot of Simulated Coins Flipping
Description
Probability plot of simulated experiments on flipping coins
Usage
coin.simu.plot(n, times, prob = NULL, qqplot = FALSE, col = "black", type = NULL,
main = NULL, sub = NULL)
Arguments
n |
number of trials in one simulation |
times |
number of simulations |
prob |
probability assigned to each possible outcome |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
col |
color of the plot |
type |
type of plot |
main |
an overall title for the plot |
sub |
a sub title for the plot |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Plot of mean value and corresponding probabilities for all simulated outcomes.
Examples
coin.simu.plot(n = 4, times = 1000, col = 'red')
coin.simu.plot(4, 1000, prob = c(0.3, 0.7), type = 'p')
Theoretical Probability Distribution of Rolling Dice
Description
Mean and probability of rolling fair or loaded dice
Usage
dice(n, prob = NULL)
Arguments
n |
number of trials |
prob |
probability assigned to each possible outcome |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Mean value and corresponding probabilities for all possible outcomes.
Examples
dice(n = 4)
dice(2, c(0.1, 0.2, 0.2, 0.1, 0.3, 0.1))
Theoretical Probability Distribution Plot of Rolling Dice
Description
Probability plot of rolling fair or loaded dice
Usage
dice.plot(n, prob = NULL, col = "black", type = NULL,
main = NULL, sub = NULL)
Arguments
n |
number of trials |
prob |
probability assigned to each possible outcome |
col |
color of the plot |
type |
type of plot |
main |
an overall title for the plot |
sub |
a sub title for the plot |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Plot of mean value and corresponding probabilities for all possible outcomes.
Examples
dice.plot(n = 4, col ='red', type = 'p')
dice.plot(3, prob = c(0.3, 0.1, 0.2, 0.1, 0.1, 0.2))
Probability Distribution of Simulated Dice Rolling
Description
Mean and probabilityf of flipping fair or loaded dice
Usage
dice.simu(n, times, prob = NULL)
Arguments
n |
number of trials in one simulation |
times |
number of simulations |
prob |
probability assigned to each possible outcome |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Mean value and corresponding probabilities for all simulated outcomes.
Examples
dice.simu(n = 4, times = 1000)
dice.simu(4, 1000, prob = c(0.3, 0.1, 0.1, 0.1, 0.3, 0.1))
Probability Distribution Plot of Simulated Dice Rolling
Description
Probability plot of dice simulated experiments
Usage
dice.simu.plot(n, times, prob = NULL, qqplot = FALSE, col = "black", type = NULL,
main = NULL, sub = NULL)
Arguments
n |
number of trials in one simulation |
times |
number of simulations |
prob |
probability assigned to each possible outcome |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
col |
color of the plot |
type |
type of plot |
main |
an overall title for the plot |
sub |
a sub title for the plot |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Plot of mean value and corresponding probabilities for all simulated outcomes.
Examples
dice.simu.plot(n = 4, times = 1000, col = 'red')
dice.simu.plot(4, 1000, prob = c(0.3, 0.1, 0.1, 0.1, 0.1, 0.3), type = 'p')
Histogram and Q-Q plot of any given continuous distribution
Description
Histogram and Q-Q plot of any given continuous distribution
Usage
distr.simu.plot(distr, n, times, prob = NULL, qqplot = FALSE, col = "black", type = NULL,
main = NULL, sub = NULL)
Arguments
distr |
vector, all possible outcomes, population distribution |
n |
number of trials in one simulation |
times |
number of simulations |
prob |
probability assigned to each possible outcome |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
col |
color of the plot |
type |
type of plot |
main |
an overall title for the plot |
sub |
a sub title for the plot |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Plot of mean value and corresponding probabilities for all simulated outcomes.
Examples
distr.simu.plot(distr = c(1,0.2,3.4,5,6.6,1.1,5,4.7,2.33,3), n = 4, times = 1000, col = 'red')
Histogram and Q-Q plot of simulated Exponential distribution
Description
Histogram and Q-Q plot of simulated Exponential distribution
Usage
expo.simu.plot(n, rate = 1, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of trials in one simulation |
rate |
vector of rates |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Exponential distribution, red curve represents theoretical density
Examples
expo.simu.plot(n = 5, rate = 2, times = 100)
Theoretical Probability Distribution of General Experiment
Description
General experiment with basic probability
Usage
expt(x, n, prob = NULL)
Arguments
x |
vector, possible outcomes in one trial of experiment |
n |
number of trials |
prob |
probability assigned to each possible outcome |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Mean value and corresponding probabilities for all possible outcomes.
Examples
expt(x = c(1:3), n = 4)
expt(c(2:4), 3, prob = c(0.3, 0.5, 0.2))
Mean square error of simulated experiments
Description
Mean square error of simulated experiments
Usage
expt.mse(x, n, times, prob = NULL)
Arguments
x |
vector, possible outcomes in one trial of experiment |
n |
number of trials |
times |
number of simulations |
prob |
probability assigned to each possible outcome |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Mean square error of simulated experiments
Examples
expt.mse(x = c(1:3), n = 4, times = 100)
expt.mse(c(0.1, 4, 2), 3, times = 50, prob = c(0.3, 0.5, 0.2))
Theoretical Probability Distribution Plot of General Experiment
Description
General experiment plot with basic probability
Usage
expt.plot(x, n, prob = NULL, col = "black", type = NULL,
main = NULL, sub = NULL)
Arguments
x |
vector, possible outcomes in one trial of experiment |
n |
number of trials |
prob |
probability assigned to each possible outcome |
col |
color of the plot |
type |
type of plot |
main |
an overall title for the plot |
sub |
a sub title for the plot |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Plot of mean value and corresponding probabilities for all possible outcomes.
Examples
expt.plot(x = c(1:3), n = 4, col ='red', type = 'p')
expt.plot(c(2:4), 3, prob = c(0.3, 0.5, 0.2))
Probability Distribution of Simulated General Experiments
Description
Mean and probability of general simulated experiments
Usage
expt.simu(x, n, times, prob = NULL)
Arguments
x |
vector, possible outcomes in one trial of experiment |
n |
number of trials in one simulation |
times |
number of simulations |
prob |
probability assigned to each possible outcome |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Mean value and corresponding probabilities for all simulated outcomes.
Examples
expt.simu(x = c(1:3), n = 4, times = 1000)
expt.simu(c(1:3), 4, 1000, prob = c(0.3, 0.1, 0.6))
Probability Distribution Plot of Simulated General Experiments
Description
Probability plot of general simulated experiments
Usage
expt.simu.plot(x, n, times, prob = NULL, qqplot = FALSE, col = "black", type = NULL,
main = NULL, sub = NULL)
Arguments
x |
vector, possible outcomes in one trial of experiment |
n |
number of trials in one simulation |
times |
number of simulations |
prob |
probability assigned to each possible outcome |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
col |
color of the plot |
type |
type of plot |
main |
an overall title for the plot |
sub |
a sub title for the plot |
Details
The default probabilty equals to 1/n. All the assigned probabilites must between 0 and 1.
Value
Plot of mean value and corresponding probabilities for all simulated outcomes.
Examples
expt.simu.plot(x = c(1:3), n = 4, times = 1000, col = 'red')
expt.simu.plot(c(1:3), 4, 1000, prob = c(0.3, 0.1, 0.6), type = 'p')
Histogram and Q-Q plot of simulated Gamma distribution
Description
Histogram and Q-Q plot of simulated Gamma distribution
Usage
gamm.simu.plot(n, shape, rate = 1, scale = 1/rate, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of trials in one simulation |
shape |
shape parameter |
rate |
vector of rates |
scale |
scale parameter |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Gamma distribution, red curve represents theoretical density
Examples
gamm.simu.plot(n = 5, shape = 3, rate = 1, times = 100)
Histogram and Q-Q plot of simulated Geometric distribution
Description
Histogram and Q-Q plot of simulated Geometric distribution
Usage
geom.simu.plot(n, prob, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of observations |
prob |
probability of success on each trial |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Geometric distribution, red curve represents theoretical density
Examples
geom.simu.plot(n = 10, prob = 0.2, times = 100)
Histogram and Q-Q plot of simulated Hypergeometric distribution
Description
Histogram and Q-Q plot of simulated Hypergeometric distribution
Usage
hyper.simu.plot(n, a, b, k, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of observations |
a |
the number of white balls in the urn |
b |
the number of black balls in the urn |
k |
the number of balls drawn from the urn |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Hypergeometric distribution, red curve represents theoretical density
Examples
hyper.simu.plot(n = 10, a = 10, b = 10, k = 5, times = 100)
Histogram and Q-Q plot of simulated Negative Binomial distribution
Description
Histogram and Q-Q plot of simulated Negative Binomial distribution
Usage
nbinom.simu.plot(n, size, prob, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of observations |
size |
number of trials (zero or more) |
prob |
probability of success on each trial |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Negative Binomial distribution, red curve represents theoretical density
Examples
nbinom.simu.plot(n = 10, size = 5, prob = 0.2, times = 100)
Histogram and Q-Q plot of simulated Normal distribution
Description
Histogram and Q-Q plot of simulated Normal distribution
Usage
normal.simu.plot(n, mean=0, sd=1, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of trials in one simulation |
mean |
vector of means |
sd |
vector of standard deviations |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Normal distribution, red curve represents theoretical density
Examples
normal.simu.plot(n = 5, mean = 3, sd =2, times = 100)
Histogram and Q-Q plot of simulated Poisson distribution
Description
Histogram and Q-Q plot of simulated Poisson distribution
Usage
pois.simu.plot(n, lambda, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of trials in one simulation |
lambda |
parameter of Poisson distribution |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Poisson distribution, red curve represents theoretical density
Examples
pois.simu.plot(n = 5, lambda = 3, times = 100)
Histogram and Q-Q plot of simulated Uniform distribution
Description
Histogram and Q-Q plot of simulated Uniform distribution
Usage
unif.simu.plot(n, min = 0, max = 1, times, ylim = NULL, qqplot = FALSE)
Arguments
n |
number of trials in one simulation |
min |
possible minimum value of Uniform distribution. Must be finite |
max |
possible maximum value of Uniform distribution. Must be finite |
times |
number of simulations |
ylim |
range of y-axis |
qqplot |
an argument to output Q-Q plot or not, can be TRUE or FALSE |
Value
Histogram and Q-Q plot of simulated Uniform distribution, red curve represents theoretical density
Examples
unif.simu.plot(n = 5, min = 3, max = 5, times = 100)