Method of Moments Estimation of Beta distribution

Description

function to get the method of moment estimate(s) of beta distribution

Usage

beta_est(
  data,
  unknown = c("shape1", "shape2", "both"),
  shape1 = NULL,
  shape2 = NULL,
  plot = TRUE,
  curvecol = "red",
  ...
)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is beta distribution

Examples

beta_est(rbeta(1000,shape1=2,shape2=1),unknown="shape2",shape1=2)#shape1 is known
beta_est(rbeta(1000,shape1=2,shape2=1),unknown="shape1",shape2=1)#shape2 is known
beta_est(rbeta(1000,shape1=2,shape2=1),unknown="both")#both will be estimated

Method of Moments Estimation of Binomial distribution

Description

function to get the method of moment estimate(s) of binomial distribution

Usage

binom_est(
  data,
  size.known = FALSE,
  size = NULL,
  plot = TRUE,
  curvecol = "red",
  ...
)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is binomial distribution

Examples

binom_est(rbinom(1000,size=5,prob=0.2),size.known=TRUE,size=5)#no of trials known
binom_est(rbinom(1000,size=10,prob=0.6))

Method of Moments Estimation of Chi-Square distribution

Description

function to get the method of moment estimate(s) of chi-square distribution

Usage

chisq_est(data, plot = TRUE, curvecol = "red", ...)

Arguments

Value

the estimated degree of freedom by the method of moments of the data assuming the underlying distribution is chi square distribution

Examples

chisq_est(rchisq(1000,df=3))

Method of Moments Estimation of Exponential Distribution

Description

function to get the method of moment estimate of exponential distribution

Usage

exp_est(data, plot = TRUE, curvecol = "red", ...)

Arguments

Value

the estimated positive rate parameter by the method of moments of the data assuming the underlying distribution is exponential distribution

Examples

exp_est(rexp(1000,rate=0.1))

Method of Moments Estimation of Gamma distribution

Description

function to get the method of moment estimate(s) of gamma distribution

Usage

gamma_est(
  data,
  unknown = c("shape", "scale", "both"),
  shape = NULL,
  scale = NULL,
  plot = TRUE,
  curvecol = "red",
  ...
)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is gamma distribution

Examples

gamma_est(rgamma(1000,shape=2,scale=1),unknown="scale",shape=2)#shape is known
gamma_est(rgamma(1000,shape=2,scale=1),unknown="shape",scale=1)#scale is known
gamma_est(rgamma(1000,shape=2,scale=1),unknown="both")#both will be estimated

Method of Moments Estimation of Negative Binomial distribution

Description

function to get the method of moment estimate(s) of negative binomial distribution

Usage

geom_est(data, plot = TRUE, curvecol = "red", ...)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is geometric distribution

Examples

geom_est(rgeom(1000,prob=0.2))

Method of Moments Estimation of Log-Normal distribution

Description

function to get the method of moment estimate(s) of log-normal distribution

Usage

lnorm_est(
  data,
  unknown = c("meanlog", "sdlog", "both"),
  meanlog = NULL,
  sdlog = NULL,
  plot = TRUE,
  curvecol = "red",
  ...
)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is log normal distribution

Examples

lnorm_est(rlnorm(1000),unknown="meanlog",sdlog=1)#meanlog unknown, but sdlog known
lnorm_est(rlnorm(1000),unknown="sdlog",meanlog=0)#sdlog unknown, but meanlog known
lnorm_est(rlnorm(1000),unknown="both")#both will be estimated

Method of Moments Estimation of Logarithmic distribution

Description

function to get the method of moment estimate(s) of logarithmic distribution

Usage

logarithmic_est(data, plot = TRUE, curvecol = "red", ...)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is logarithmic distribution

Examples

require(actuar)
logarithmic_est(rlogarithmic(1000,prob=0.6))

A object structure of class momint

Description

A object structure of class momint

Usage

momint(dist, pop.par, FUN, n, conf.coeff, c)

Arguments

Value

It doesn't return anything directly, it is used to print the output of another function

A structure of class momtest

Description

A structure of class momtest

Usage

momtest(
  data,
  null.dist,
  null.par,
  alter.dist,
  alter.par,
  n,
  conf.level,
  d,
  power
)

Arguments

Value

It doesn't return anything directly, it just used as output of the testing in this package

Method of Moments Estimation of Negative Binomial distribution

Description

function to get the method of moment estimate(s) of negative binomial distribution

Usage

nbinom_est(
  data,
  size.known = FALSE,
  size = NULL,
  plot = TRUE,
  curvecol = "red",
  ...
)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is negative binomial distribution

Examples

nbinom_est(rnbinom(1000,size=5,prob=0.2),size.known=TRUE,size=5)#no of successes known
nbinom_est(rnbinom(1000,size=10,prob=0.6))

Method of Moments Estimation of Normal distribution

Description

function to get the method of moment estimate(s) of normal distribution

Usage

norm_est(
  data,
  unknown = c("mean", "sd", "both"),
  mean = NULL,
  sd = NULL,
  plot = TRUE,
  curvecol = "red",
  ...
)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is normal distribution

Examples

norm_est(rnorm(1000),unknown="mean",sd=1)#mean unknown, but sd known
norm_est(rnorm(1000),unknown="sd",mean=0)#sd unknown, but mean known
norm_est(rnorm(1000),unknown="both")#both will be estimated

Method of Moments Estimation of Poisson distribution

Description

function to get the method of moment estimate(s) of poisson distribution

Usage

pois_est(data, plot = TRUE, curvecol = "red", ...)

Arguments

Value

the estimated parameters by the method of moments of the data assuming the underlying distribution is poisson distribution

Examples

pois_est(data=rpois(1000,lambda=2),plot=TRUE)
pois_est(data=rpois(1000,lambda=0.2),plot=FALSE)#will not give the plot

Most Powerful Test by Neyman-Pearson Lemma

Description

It can be used to check whether a data comes from null distribution or from the alternative distribution

Usage

sim_mp_test(
  data,
  null.dist = c("uniform", "normal", "lognormal", "gamma", "cauchy", "pareto", "weibull",
    "rayleigh", "laplace", "beta", "binomial", "poisson", "negativebinomial",
    "geometric", "t", "f", "logarithmic"),
  null.par,
  alter.dist = c("uniform", "normal", "lognormal", "gamma", "cauchy", "pareto",
    "weibull", "rayleigh", "laplace", "beta", "binomial", "poisson", "negativebinomial",
    "geometric", "t", "f", "logarithmic"),
  alter.par,
  test.level = 0.95,
  sim.size = 1,
  power = TRUE
)

Arguments

Details

This function mainly test whether data comes from the null distribution or alternative distribution. It uses the theory of the Most Powerful (MP) test. It basically uses simulation to get the p value and make the decision. Increasing sim.size give more accuracy as well as test can be failed if you increase it heavily.

Value

A list of class "momtest" will be returned having the following components:

Method

The Method's Name

Data

The first 6 elements of input data

Null.Distrbution

The family of null distribution

Null.Parameter

The parameter values of the null distribution

Alternative.Distrbution

The family of alternative distribution

Alternative.Parameter

The parameter values of the alternative distribution

Sample.Size

The sample size

Significance.level

The level of the significance of the test

Decision

The Test Result, wheter the null hypotheis is rejected or not

Power

Power of the Test

Examples

sim_mp_test(rnorm(100),null.dist="normal",null.par=c(0,1),alter.dist="cauchy",alter.par=c(0,1))
sim_mp_test(rnorm(100),null.dist="nor",null.par=c(2,1),alter.dist="nor",alter.par=c(0,1))

Simulated confidence interval of a statistic

Description

A function that returns a sampling interval for a statistic formed from random sample of certain probability distributions. The function generates the confidence interval using Monte Carlo simulations. The results might be unreliable if the resulting statistic has fat tailed distribution.

Usage

sim_sam_int(
  dist = c("normal", "lognormal", "gamma", "chisquare", "cauchy", "pareto", "weibull",
    "rayleigh", "laplace", "beta", "binomial", "poisson", "negativebinomial",
    "geometric", "t", "f", "uniform"),
  pop.par,
  FUN,
  side = c("lower", "upper", "both"),
  conf.coeff = 0.95,
  range = 1,
  n = 100,
  sim.size = 1000
)

Arguments

Details

The function asks the user to specify a distribution from which random sample is drawn and to specify a function of the random variables for which an approximate sampling Interval is to be provided. The function then uses Monte Carlo simulation technique to provide an approximate sampling interval of the statistic. This function might be useful when the sampling distribution for a particular statistic is unknown, but that statistic might be useful in drawing meaningful inference. Although this function is inferior to other sophisticated techniques to deal with this problem, it might come handy for a beginner.

Value

A list of class "momint" will be returned having the following components:

Method

The Method's Name

Population.Distrbution

The family of population distribution

Paramater

The parameter values of the population distribution

Statistic

The function of which the interval will be provided

Sample.Size

The sample size

Confidence.Coefficient

The confidence coefficient of the sampling interval

Sampling.Interval

The estimated sampling interval

Examples

sim_sam_int(dist="normal",pop.par=c(0,1),FUN=mean,side="both")
sim_sam_int(dist="binomial",pop.par=c(5,0.5),FUN=sum,side="lower")