**Package: **prob**Superclasses: **prob.TruncatableDistribution

Kernel probability distribution object

`prob.KernelDistribution`

is an object consisting
of parameters, a model description, and sample data for a nonparametric
kernel-smoothing distribution. Create a `prob.KernelDistribution`

object
using `fitdist`

or `dfittool`

.

creates
a probability distribution object by fitting a kernel-smoothing distribution
to the data in `pd`

= fitdist(`x`

,'Kernel')`x`

.

creates
a probability distribution object with additional options specified
by one or more name-value pair arguments. For example, you can change
the kernel function or specify the kernel bandwidth.`pd`

= fitdist(`x`

,'Kernel',`Name,Value`

)

mean | Mean of probability distribution object |

negloglik | Negative loglikelihood |

std | Standard deviation of probability distribution object |

var | Variance of probability distribution object |

cdf | Cumulative distribution function of probability distribution object |

icdf | Inverse cumulative distribution function of probability distribution object |

iqr | Interquartile range of probability distribution object |

median | Median of probability distribution object |

Probability density function of probability distribution object | |

random | Generate random numbers from probability distribution object |

truncate | Truncate probability distribution object |

The kernel distribution is a nonparametric estimation of the probability density function (pdf) of a random variable.

The kernel distribution uses the following options.

Option | Description | Possible Values |
---|---|---|

`Kernel` | Kernel function type | `normal` , `box` , `triangle` , `epanechnikov` |

`BandWidth` | Kernel smoothing parameter | `BandWidth > 0` |

The kernel density estimator is

$${\widehat{f}}_{h}\left(x\right)=\frac{1}{nh}{\displaystyle \sum _{i=1}^{n}K\left(\frac{x-{x}_{i}}{h}\right)}\text{\hspace{1em}};\text{\hspace{1em}}-\infty <x<\infty \text{\hspace{0.17em}},$$

where *n* is
the sample size, $$K(\xb7)$$ is the kernel
function, and *h* is the bandwidth.

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