Fit Word Length Data to Distributions
The length of words in English follows a BinomialDistribution.
worddata = StringLength /@ DictionaryLookup[{"English", All}];binom = EstimatedDistribution[worddata, BinomialDistribution[n, p], ParameterEstimator -> {"MaximumLikelihood", Method -> {"FindRoot", MaxIterations -> 1000}}];Show[Histogram[worddata, {Range[25] - 1 / 2}, "ProbabilityDensity", ChartStyle -> "SolarColors", BaseStyle -> {FontFamily -> "Verdana"}, PlotLabel -> "Length of Words in English"], DiscretePlot[PDF[binom, x], {x, 0, 25}, PlotRange -> All, PlotStyle -> Black, PlotMarkers -> {Automatic, Medium}], Epilog -> Inset[Framed[Style[Grid[{{"Estimated Distribution:"}, {binom}}], 12], Background -> StandardBlue, RoundingRadius -> 3], {Right, 0.15}, {Right, Top}], ImageSize -> 400]