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Maximum Likelihood Parameter Estimation

Source: R/fit-mle.R
fit_mle.Rd

Estimates the parameters of a probability distribution by maximizing the log‐likelihood. Initial parameter estimates are obtained using the method of L‐moments and optimization is performed via stats::nlminb() with repeated perturbations if needed.

For NS-FFA: To estimate parameters for a nonstationary model, include the observation years (ns_years) and the nonstationary model structure (ns_structure).

Usage

fit_mle(data, distribution, ns_years = NULL, ns_structure = NULL)

Arguments

data

Numeric vector of observed annual maximum series values. Must be strictly positive, finite, and not missing.

distribution

A three-character code indicating the distribution family. Must be "GUM", "NOR", "LNO", "GEV", "GLO", "GNO", "PE3", "LP3", or "WEI".

ns_years

For NS-FFA only: Numeric vector of observation years corresponding to data. Must be the same length as data and strictly increasing.

ns_structure

For NS-FFA only: Named list indicating which distribution parameters are modeled as nonstationary. Must contain two logical scalars:

  • location: If TRUE, the location parameter has a linear temporal trend.

  • scale: If TRUE, the scale parameter has a linear temporal trend.

Value

A list containing the results of parameter estimation:

  • data: The data argument.

  • distribution: The distribution argument.

  • ns_years: The ns_years argument, if given.

  • ns_structure: The ns_structure argument, if given.

  • method: "MLE".

  • params: Numeric vector of estimated parameters.

  • mll: The maximum value of the log‐likelihood.

Details

  1. Calls fit_lmoments() on data to obtain initial parameter estimates.

  2. Initializes trend parameters to zero if necessary.

  3. For WEI models, sets the location parameter to zero to ensure support.

  4. Defines an objective function using utils_log_likelihood().

  5. Runs stats::nlminb() with box constraints. Attempts minimization up to 100 times.

See also

utils_log_likelihood(), fit_lmoments(), stats::nlminb()

Examples

data <- rnorm(n = 100, mean = 100, sd = 10)
ns_years <- seq(from = 1901, to = 2000)
ns_structure <- list(location = TRUE, scale = FALSE)
fit_mle(data, "GNO", ns_years, ns_structure)
#> $data
#>   [1] 102.26379 108.00647  94.50523  87.72731  99.77925 108.63950 112.97008
#>   [8]  96.02339  84.07061 102.54378  82.27624 100.78716  86.00637 132.19060
#>  [15]  91.81452 100.36118  94.42961  91.78141 112.85518  87.10887  98.47703
#>  [22]  90.29603 115.85079  96.85944  90.73756 113.84408  89.75266  84.38758
#>  [29] 103.32694  83.67615 110.88718 105.92150  88.93916  97.37292 105.86291
#>  [36]  91.23258 108.51698  99.39284  95.83097 107.19835  85.08089 100.34346
#>  [43]  97.53211 119.54145 100.09658 113.11216  88.64854  95.31387 103.40441
#>  [50]  98.21043 116.15922  99.69659 110.39512 102.20352 109.53315 111.88895
#>  [57]  95.33576 116.22845  92.46341 108.04747  93.51511  94.71189  76.80314
#>  [64] 111.49970  97.32005 113.35798 103.04911 110.48993  92.94706 100.24797
#>  [71] 100.81656 105.06131  94.48316 107.03604 101.50665  81.50408  96.53061
#>  [78]  99.56023  98.79920  92.41629 110.41362 100.44308 108.27265  98.96216
#>  [85]  92.11579 108.29480 116.68956 102.13646 111.57535  89.21120 113.15584
#>  [92]  93.25724  93.56120 100.40112 108.21379 114.65366 104.47294 103.40752
#>  [99] 120.89891 103.25784
#> 
#> $distribution
#> [1] "GNO"
#> 
#> $ns_years
#>   [1] 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915
#>  [16] 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930
#>  [31] 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945
#>  [46] 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960
#>  [61] 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975
#>  [76] 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
#>  [91] 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
#> 
#> $ns_structure
#> $ns_structure$location
#> [1] TRUE
#> 
#> $ns_structure$scale
#> [1] FALSE
#> 
#> 
#> $prior
#> NULL
#> 
#> $method
#> [1] "MLE"
#> 
#> $params
#> [1] 97.08225431  6.57788171  9.78909788 -0.08641844
#> 
#> $mll
#> [1] -370.0208
#>