Mod()
See “Modulo(number, divisor)” on page 126
Modulo(number, divisor) Mod(number, divisor)
Description
Returns the remainder when number is divided by divisor.
Examples Modulo(6,5)
1
Round(n, places) Description
Rounds n to number of decimal places given.
Probability Functions
Beta Density(x, alpha, beta, <theta>, <sigma>) Description
Calculates the beta probability density function (pdf).
Returns
The density function at quantile x for the beta distribution for the given arguments.
Arguments
x A quantile between theta and theta + sigma. Theta’s default value is 0. Sigma’s default value is 1.
alpha, beta Shape parameters that must both be greater than 0.
theta optional threshold. The allowable range is . The default is 0.
sigma optional scale parameter, which must be greater than 0. The default is 1.
See Also
The section on probability functions in the Using JMP book.
Beta Distribution(x, alpha, beta, <theta>, <sigma>) Description
Calculates the cumulative distribution function for the beta distribution.
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Returns
Returns the cumulative distribution function at quantile x for the beta distribution with shape arguments alpha and beta.
Arguments
x A quantile between theta and theta + sigma.
alpha, beta Shape parameters that must both be greater than 0.
theta optional threshold. The allowable range is . The default is 0.
sigma optional scale parameter, which must be greater than 0. The default is 1.
See Also
The section on probability functions in the Using JMP book.
Beta Quantile(p, alpha, beta, <theta>, <sigma>) Description
Calculates the requested quantile for the beta distribution.
Returns
Returns the pth quantile from the beta distribution with shape arguments alpha and beta.
Arguments
p The probability of the quantile desired; p must be between 0 and 1.
alpha, beta Shape parameters that must both be greater than 0.
theta optional threshold. The allowable range is . The default is 0.
sigma optional scale parameter, which must be greater than 0. The default is 1.
See Also
The section on probability functions in the Using JMP.
ChiSquare Density(q, df, <center>) Description
The chi-square density at q of the chi-square with df degrees of freedom and optional non-centrality parameter center.
Returns
The chi-square density.
Arguments q quantile
df degrees of freedom.
center non-centrality parameter
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ChiSquare Distribution(q, df, <center>) Description
Returns cumulative distribution function at quantile x for chi-square with df degrees of freedom centered at center.
ChiSquare Quantile(q, df, <center>) Description
Returns the pth quantile from the chi-square distribution with df degrees of freedom, centered at center.
Dunnett P Value(q, nTrt, dfe, lambdaVec) Description
Returns the p-value from Dunnett’s multiple comparisons test.
Returns
A number that is the p-value.
Arguments
q A number that is the test statistic.
nTrt The number of treatments being compared to the control treatment.
dfe The error degrees of freedom.
lambdaVec A vector of parameters. If lambdaVec is missing (.), the parameters are set to 1/Sqrt(2).
Dunnett Quantile(1-alpha, nTrt, dfe, lambdaVec) Description
Returns quantile needed in from Dunnett’s multiple comparisons test.
Returns
A number that is the quantile.
Arguments
1-alpha A number that is the confidence level.
nTrt The number of treatments being compared to the control treatment.
dfe The error degrees of freedom.
lambdaVec A vector of parameters. If lambdaVec is missing (.), the parameters are set to 1/Sqrt(2).
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F Density(x, dfnum, dfden, <center>) Description
Returns the F density at x for the F distribution with numerator and denominator degrees of freedom dfnum and dfden, with optional noncentrality parameter center.
F Distribution(x, dfnum, dfden, <center>) Description
Returns cumulative distribution function at quantile x for F distribution with numerator and denominator degrees of freedom dfnum and dfden and noncentrality parameter center.
F Power(alpha, dfh, dfm, d, n) Description
Calculates the power from a given situation involving an F test or a t test.
F Quantile(x, dfnum, dfden, <center>) Description
Returns the pth quantile from the F distribution with numerator and denominator degrees of freedom dfnum and dfden and noncentrality parameter center.
F Sample Size(alpha, dfh, dfm, d, power) Description
Calculates the sample size from a given situation involving an F test or a t test.
Frechet Density(x, mu, sigma) Description
Returns the density at x of a Frechet distribution with location mu and scale sigma.
Arguments x A number.
mu A location.
sigma The scale.
Frechet Distribution(x, mu, sigma) Description
Returns the probability that the Fréchet distribution with location mu and scale sigma is less than x.
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Arguments x A number.
mu A location.
sigma The scale.
Frechet Quantile(p, mu, sigma) Description
Returns the quantile associated with a cumulative probability p for a Fréchet distribution with location mu and scale sigma.
Arguments
p The probability of the quantile desired; p must be between 0 and 1.
mu A location.
sigma The scale.
Gamma Density(q, alpha, <scale>, <threshold>) Description
Calculates the density at q of a Gamma probability distribution.
Returns
The density function at quantile q for the gamma density distribution for the given arguments.
Arguments q A quantile.
alpha Shape parameters that must be greater than 1.
scale Optional scale, which must be greater than 0. The default is 1.
threshold Optional threshold parameter. The allowable range is . The default is 0.
See Also
The section on probability functions in the Using JMP.
Gamma Distribution(x, <shape, scale, threshold>) IGamma(x, <shape, scale, threshold>)
Description
Returns cumulative distribution function at quantile x for the gamma distribution with shape, scale, and threshold given.
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Gamma Quantile(p, <shape, scale, threshold>) Description
Returns the pth quantile from the gamma distribution with the shape, scale, and threshold parameters given.
GLog Density(q, mu, sigma, lambda) Description
Returns the density at q of a generalized logarithmic distribution with location mu, scale sigma, and shape lambda.
GLog Distribution(q, mu, sigma, lambda) Description
Returns the probability that a generalized logarithmically distribution random variable is less than q.
GLog Quantile(p, mu, sigma, lambda) Description
Returns the quantile for whose value the probability is p that a random value would be lower.
IGamma()
See “Gamma Distribution(x, <shape, scale, threshold>)” on page 130.
Johnson Sb Density(q, gamma, delta, theta, sigma) Description
Returns the density at q of a Johnson Sb distribution.
Arguments
q A value that is in the interval theta to theta + sigma.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Scale parameter that must be greater than 0.
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Johnson Sb Distribution(q, gamma, delta, theta, sigma) Description
Returns the probability that a Johnson Sb-distributed random variable is less than q.
Arguments
q A value that is in the interval theta to theta + sigma.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Scale parameter that must be greater than 0.
Johnson Sb Quantile(p, gamma, delta, theta, sigma) Description
Returns the quantile whose value for which the probability is p that a random value would be lower.
Arguments
p The probability of the quantile desired; p must be between 0 and 1.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Scale parameter that must be greater than 0.
Johnson Sl Density(q, gamma, delta, theta, sigma) Description
Returns the density at q of a Johnson Sl distribution.
Arguments
q A value that is in the interval theta to +infinity.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Parameter that defines if the distribution is skewed positively or negatively. Sigma must be equal to either +1 (skewed positively) or -1 (skewed negatively).
Johnson Sl Distribution(q, gamma, delta, theta, sigma) Description
Returns the probability that a Johnson Sl-distributed random variable is less than q.
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Arguments
q A value that is in the interval theta to +infinity.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Parameter that defines if the distribution is skewed positively or negatively. Sigma must be equal to either +1 (skewed positively) or -1 (skewed negatively).
Johnson Sl Quantile(p, gamma, delta, theta, sigma) Description
Returns the quantile whose value for which the probability is p that a random value would be lower.
Arguments
p The probability of the quantile desired; p must be between 0 and 1.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Parameter that defines if the distribution is skewed positively or negatively. Sigma must be equal to either +1 (skewed positively) or -1 (skewed negatively).
Johnson Su Density(q, gamma, delta, theta, sigma) Description
Returns the density at q of a Johnson Su distribution.
Arguments
q A value that is between -infinity and +infinity.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Scale parameter that must be greater than 0.
Johnson Su Distribution(q, gamma, delta, theta, sigma) Description
Returns the probability that a Johnson Su-distributed random variable is less than q.
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Arguments
q A value that is between -infinity and +infinity.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Scale parameter that must be greater than 0.
Johnson Su Quantile(p, gamma, delta, theta, sigma) Description
Returns the quantile whose value for which the probability is p that a random value would be lower.
Arguments
p The probability of the quantile desired; p must be between 0 and 1.
gamma Shape parameter that can be any value.
delta Shape parameter that must be greater than 0.
theta Location parameter that can be any value.
sigma Scale parameter that must be greater than 0.
LEV Density(x, mu, sigma) Description
Returns the density at x of the largest extreme value distribution with location mu and scale sigma.
LEV Distribution(x, mu, sigma) Description
Returns the probability that the largest extreme value distribution with location mu and scale sigma is less than x.
LEV Quantile(p, mu, sigma) Description
Returns the quantile associated with a cumulative probability p of the largest extreme value distribution with location mu and scale sigma.
Logistic Density(x, mu, sigma) Description
Returns the density at x of a logistic distribution with location mu and scale sigma.
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Logistic Distribution(x, mu, sigma) Description
Returns the probability that the logistic distribution with location mu and scale sigma is less than x.
Logistic Quantile(x, mu, sigma) Description
Returns the quantile associated with a cumulative probability p of the logistic distribution with location mu and scale sigma.
Loglogistic Density(x, mu, sigma) Description
Returns the density at x of a loglogistic distribution with location mu and scale sigma.
Loglogistic Distribution(x, mu, sigma) Description
Returns the probability that the loglogistic distribution with location mu and scale sigma is less than x.
Loglogistic Quantile(x, mu, sigma) Description
Returns the quantile associated with a cumulative probability p of the loglogistic distribution with location mu and scale sigma.
Lognormal Density(x, mu, sigma) Description
Returns the density at x of a lognormal distribution with location mu and scale sigma.
Lognormal Distribution(x, mu, sigma) Description
Returns the probability at x of a lognormal distribution with location mu and scale sigma.
Lognormal Quantile(x, mu, sigma) Description
Returns the quantile at p of a lognormal distribution with location mu and scale sigma.
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Normal Biv Distribution(x, y, r, <mu1>, <s1>, <mu2>, <s2>) Description
Computes the probability that an observation (X, Y) is less than or equal to (x, y) with correlation coefficient r where X is individually normally distributed with mean mu1 and standard deviation s1 and Y is individually normally distributed with mean mu2 and standard deviation s2. If mu1, s1, mu2, and s2 are not given, the function assumes the standard normal bivariate distribution with mu1=0, s1=1, mu2=0, and s2=1.
Normal Density(x, <mean>, <stddev>) Description
Returns the value of the density function at quantile x for the normal distribution with mean and stddev. The default mean is 0. the default stddev is 1.
Normal Distribution(x, <mean>, <stddev>) Description
Returns the cumulative distribution function at quantile x for the normal distribution with mean and stddev. The default mean is 0. the default stddev is 1.
Normal Mixture Density(q, mean, stdev, probability) Description
Returns the density at q of a normal mixture distribution with group means mean, group standard deviations stdev, and group probabilities probability. The mean, stdev, and probability arguments are all vectors of the same size.
Normal Mixture Distribution(q, mean, stdev, probability) Description
Returns the probability that a normal mixture distributed variable with group means mean, group standard deviations stdev, and group probabilities probability is less than q. The mean, stdev, and probability arguments are all vectors of the same size.
Normal Mixture Quantile(p, mean, stdev, probability) Description
Returns the quantile, the values for which the probability is p that a random value would be lower. The mean, stdev, and probability arguments are all vectors of the same size.
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Normal Quantile(p, <mean>, <stddev>) Probit(p, <mean>, <stddev>)
Description
Returns the pth quantile from the normal distribution with mean and stddev. The default mean is 0. the default stddev is 1.
Probit()
See “Normal Quantile(p, <mean>, <stddev>)” on page 137.
SEV Density(x, mu, sigma) Description
Returns the density at x of the smallest extreme distribution with location mu and scale sigma.
SEV Distribution(x, mu, sigma) Description
Returns the probability that the smallest extreme distribution with location mu and scale sigma is less than x.
SEV Quantile(p, mu, sigma) Description
Returns the quantile at p of the smallest extreme distribution with location mu and scale sigma.
Students t Density()
See “t Density(q, df)” on page 138.
Students t Distribution()
See “t Distribution(q, df, <nonCentrality>)” on page 138.
Students t Quantile()
See “t Quantile(p, df, <nonCentrality>)” on page 138.
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t Density(q, df)
Students t Density(q, df) Description
Returns the value of the density function at quantile x for the Student’s t distribution with degrees of freedom df.
t Distribution(q, df, <nonCentrality>)
Students t Distribution(q, df, <nonCentrality>) Description
Returns the probability that a Student’s t distributed random variable is less than q.
NonCentrality defaults to 0.
t Quantile(p, df, <nonCentrality>)
Students t Quantile(p, df, <nonCentrality>) Description
Returns the pth quantile from the Student’s t distribution with degrees of freedom df.
NonCentrality defaults to 0.
Tukey HSD P Value(q, n, dfe) Description
Returns the p-value from Tukey’s HSD multiple comparisons test.
Arguments
q The test statistic.
n The number of groups in the study.
dfe The error degrees of freedom, based on the total study sample.
Tukey HSD Quantile(1-alpha, n, dfe) Description
Returns the quantile needed in Tukey’s HSD multiple comparisons test.
Arguments
1-alpha The confidence level.
n The number of groups in the study.
dfe The error degrees of freedom, based on the total study sample.
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Weibull Density(x, shape, <scale, threshold>) Description
Returns the value of the density function at quantile x for the Weibull distribution with the parameters given.
Weibull Distribution(x, shape, <scale, threshold>) Description
Returns the cumulative distribution function at quantile x for the Weibull distribution with the parameters given.
Weibull Quantile(p, shape, <scale, threshold>) Description
Returns the pth quantile from the Weibull distribution with the parameters given.