Package-level declarations
Types
Estimates the parameters of the beta distribution via the method of moments. Formulas can be found in:
Estimates the probability of success (p) and number of trials (n) for the binomial distribution based. The number of trials is estimated based on the maximum observed value adjusted based on range estimation for uniform(min, max) distribution.
Estimates the probability of success (p) and number of trials (n) for the binomial distribution based on the method of moments. The data must not contain negative values. The estimation process assumes that the supplied data are integer valued counts over the range {0,1,2,..., n}. That is this parameterization represents the number of success in n trials. To ensure moment matching, the estimation process does not ensure that n is integer valued.
Uses the sample average of the observations, which is the MLE estimator. The data must not contain negative values.
Estimates the parameters of the Gamma distribution based on a MLE algorithm. See page 285-286 of Law (2007) Simulation Modeling and Analysis. Uses bi-section search seeded by initial estimates based on MOM estimates. Convergence is not guaranteed and will be indicated in the EstimatedParameters success property and the message. Requires that the data be strictly positive and that there are at least two observations. Also, requires that all the supplied data are not equal. The user may vary some of the search control parameters to assist with convergence.
Estimates the shape and scale of a gamma distribution based on the method of moments. Observations must be greater than or equal to zero and must not all be equal. There must be at least two observations. The sample average and sample variance of the observations must be strictly greater than zero.
Uses the sample median and the mean absolute deviation from the median, which are the MLE estimators. There must be at least two observations. The parameter names are location and scale
Estimates the location and scale of a logistic distribution based on the method of moments. Observations must not all be equal. There must be at least two observations. The moment matching is based on an unbiased estimate of the variance.
Takes the natural logarithm of the data and then estimates the mean and variance of the associated normal distribution. Then the parameters are converted to the mean and variance of the lognormal distribution. The supplied data must be strictly positive and their must be at least 2 observations.
Estimates the probability of success (p) and number of successes (r) until the trials stop for the negative binomial distribution based on the method of moments. The data must not contain negative values. The estimation process assumes that the supplied data are integer valued counts over the range {0,1,2,...}. That is this parameterization represents the number of failures until the rth success. To ensure moment matching, the estimation process does not ensure that r is integer valued.
Uses the sample average and sample variance of the data, which are the MLE estimators. There must be at least two observations.
This interface defines a general function that uses 1-dimensional data, and estimates the parameters of some uni-variate distribution via some estimation algorithm.
Estimates the parameters of the Pearson Type 5 distribution based on a MLE algorithm. See page 293-294 of Law (2007) Simulation Modeling and Analysis. Uses bi-section search seeded by initial estimates based on MOM estimates. Convergence is not guaranteed and will be indicated in the EstimatedParameters success property and the message. Requires that the data be strictly positive and that there are at least two observations. Also, requires that all the supplied data are not equal. The user may vary some of the search control parameters to assist with convergence. The algorithm relies on the fact if X ~ PT5(shape, scale) if and only if 1/X ~ gamma(shape, 1/scale). Thus, the data is transformed as 1/X, and a gamma distribution is fit. If the MLE of the gamma is successful the correct parameters are returned.
Uses the sample average of the observations, which is the MLE estimator. The data must not contain negative values. The estimation process assumes that the supplied data are integer valued counts over the range {0,1,2,...}
The approach is based on estimating the min and max via the recommended approach for the uniform distribution. Then, the mode is estimated by solving for it in terms of the sample average.
Uses the minimum unbiased estimators based on the order statistics. See: 1. Castillo E, Hadi AS. A method for estimating parameters and quantiles of distributions of continuous random variables. Computational Statistics & Data Analysis. 1995 Oct;20(4):421–39. There must be at least two observations and the observations cannot all be the same.
Estimates the parameters of the Weibull distribution based on a MLE algorithm. See page 287-288 of Law (2007) Simulation Modeling and Analysis. Uses Newton steps followed by bi-section search (if needed). Convergence is not guaranteed and will be indicated in the EstimatedParameters success property and the message. Requires that the data be strictly positive and that there are at least two observations. Also, requires that all the supplied data are not equal. The user may vary some of the search control parameters to assist with convergence.
Applies the percentile method to estimating the parameters of the Weibull distribution as outline in these papers: