Lognormal
Models the lognormal distribution This distribution is commonly used to model the time of a task
Parameters: mean and variance.
Note: these parameters are the actual mean and variance of the lognormal distribution, not some underlying normal distribution as in many implementations.
Parameters
must be > 0
must be > 0
an optional name/label
Constructors
Properties
The mean of the underlying normal
The standard deviation of the underlying normal
The variance of the underlying normal
the parameters for this type of random variable
Functions
Returns an array of probabilities each representing F(x_i). The CDF is evaluated for each point in the input array x and the probabilities are returned in the returned array.
Returns the probability of being in the interval, F(upper limit) - F(lower limit) Be careful, this is Pr{lower limit < = X < = upper limit} which includes the lower limit and has implications if the distribution is discrete
Returns the Pr{x1 <= X <= x2} for the distribution. Be careful, this is Pr{x1 <= X <= x2} which includes the lower limit and has implications if the distribution is discrete
Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function
Computes the complementary cumulative probability distribution function for given value of x. This is P{X > x}
Computes the first order loss function for the function for given value of x, G1(x) = Emax(X-x,0)
Computes x_p where P(X <= x_p) = p for the supplied array of probabilities. Requires that the values within the supplied array are in (0,1)
Provides the inverse cumulative distribution function for the distribution
Assuming that the observations in the array data are from a random sample, this function computes the likelihood function. This is computed using as the sum of the log-likelihood function raised to e. Implementation may want to specify other computationally efficient formulas for this function or (most likely) the sum of the log-likelihood function.
Computes the natural log of the pdf function evaluated at x. Implementations may want to specify computationally efficient formulas for this function.
Gets the parameters for the distribution
Sets the parameters for the distribution mean = parameters0 and variance = parameters1
Sets the parameters of a lognormal distribution to mean and variance. Note: these parameters are the actual mean and variance of the lognormal, not the underlying normal as in many other implementations.
Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)Emax(X-x,0)*max(X-x-1,0)
Returns the standard deviation for the distribution as the square root of the variance if it exists
Computes the sum of the log-likelihood function evaluated at each observation in the data. Implementations may want to specify computationally efficient formulas for this function.