Details

For SmoothKernelDistribution, the option MaxExtraBandwidths can be used to determine the extent to which the estimate will extend beyond the data.
Typical settings include:
smooth bandwidths beyond the data

${r_(min),r_(max)}$ smooth and above and below the data

${rspec_(1),rspec_(2),...}$ Use for smoothing in dimension
By default is used.

Examples

Truncate the estimate prior to smoothing for skewed distributions:

Wolfram Language code: data = RandomVariate[ExponentialDistribution[1], 1000];

Wolfram Language code:

𝒟1 = SmoothKernelDistribution[data, MaxExtraBandwidths -> {12, 12}];
𝒟2 = SmoothKernelDistribution[data, MaxExtraBandwidths -> {0, 12}];

Wolfram Language code: Table[Plot[PDF[𝒟, x], {x, -2, 10}, PlotRange -> All, Frame -> True, Exclusions -> None], {𝒟, {𝒟1, 𝒟2}}]

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		smooth bandwidths beyond the data
	${r_(min),r_(max)}$	smooth and above and below the data
	${rspec_(1),rspec_(2),...}$	Use for smoothing in dimension