# Wolfram Language™

## Faster Distribution Estimation

Version 11 adds numerous improvements to distribution estimation, especially in performance. The following charts show the timings for estimating several distributions with different sample sizes. Experiments were performed on a Windows 10 system with an Intel Xeon Processor E3-1245 v2 3.40 GHz. The number at the bottom shows how much faster Version 11 is than Version 10.

Student distribution.

show complete Wolfram Language input
In:= ```dist = StudentTDistribution[loc, sc, df]; ndist = StudentTDistribution[-1, 1, 2]; Table[ sample = BlockRandom[SeedRandom["MarketingExample"]; RandomVariate[ndist, n]]; Mean[Table[ First[AbsoluteTiming[EstimatedDistribution[sample, dist];]], {5}]] , {n, {10, 100, 1000}}] ```
Out= Weibull distribution.

show complete Wolfram Language input
In:= ```dist = WeibullDistribution[al, be]; ndist = WeibullDistribution[3, 2]; Table[ sample = BlockRandom[SeedRandom["MarketingExample"]; RandomVariate[ndist, n]]; Mean[Table[ First[AbsoluteTiming[EstimatedDistribution[sample, dist];]], {5}]] , {n, {10, 100, 1000}}]```
Out= Mixture of binormal distributions.

show complete Wolfram Language input
In:= ```dist = MixtureDistribution[{w1, w2}, {BinormalDistribution[{m11, m12}, {s11, s12}, \[Rho]1], BinormalDistribution[{m21, m22}, {s21, s22}, \[Rho]2]}]; ndist = MixtureDistribution[{0.3, 0.7}, {BinormalDistribution[{0, 1}, {0.5, 0.25}, 0.7], BinormalDistribution[{-0.5, 0}, {0.5, 0.25}, 0.1]}]; Table[ sample = BlockRandom[SeedRandom["MarketingExample"]; RandomVariate[ndist, n]]; Mean[Table[ First[AbsoluteTiming[ TimeConstrained[EstimatedDistribution[sample, dist];, 100]]], {5}]] , {n, {10, 100, 1000}}]```
Out= Multivariate distribution.

show complete Wolfram Language input
In:= ```dist = MultivariateTDistribution[{{m11, m12}, {m21, m22}}, n]; ndist = MultivariateTDistribution[{{1, 1/3}, {1/3, 1}}, 10]; Table[ sample = BlockRandom[SeedRandom["MarketingExample"]; RandomVariate[ndist, n]]; Mean[Table[ First[AbsoluteTiming[EstimatedDistribution[sample, dist];]], {5}]] , {n, {10, 100, 1000}}]```
Out= 