Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

**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.

Was this topic helpful?