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From |
"Nick Cox" <[email protected]> |

To |
<[email protected]> |

Subject |
RE: st: RE: Histograms (was: Multiple (overlaid) Histogram) |

Date |
Fri, 30 May 2003 20:58:16 +0100 |

Marcello Pagano > As I have said before, I would very much like, with Allan Reese, an > option for equi-probability histograms. I think that this > is especially > useful when thinking of the histogram as an estimator of an > underlying > density function of a continuous variable. I do not see a strong > argument, other than tradition (laziness?), for being > constrained to > histograms with equi-spaced bins. An interesting problem. I see one key question arising. If I understand this properly, we just need to find so many quantiles x_(i) equally spaced on the probability scale and calculate bar heights proportional to 1 / (x_(i+1) - x_(i)). In practice, it is not that uncommon to get ties, implying infinite bar heights. We can fudge this by interpolating linearly between different quantiles. What lies below is a hack. The number of bins is wired in at no more than 20. My experiments indicate that you need a lot of data to avoid somewhat bizarre details. Essentially you are bound to see the kind of instability inherent in crude numerical derivatives. Don't point out that density estimates are nicer! I know that. This is an attempt at what Marcello wants. Nick [email protected] Example: sysuse auto foreach v of var price-gear { eqprhistogram `v' more } program eqprhistogram *! for Marcello, eppur si muove! *! NJC 1.0.0 30 May 2003 version 8 syntax varname(numeric) [if] [in] [ , bin(numlist int >0 <=20) * ] // #bins <= 20 if "`bin'" == "" local bin = 20 local binp1 = `bin' + 1 local binm1 = `bin' - 1 // enough data? marksample touse qui count if `touse' if `r(N)' < `binp1' { di as err "insufficient observations" error 2000 } tempvar quantile qnum qid qadd width x height id qui { // get quantiles su `varlist' if `touse', meanonly generate `quantile' = r(min) in 1 replace `quantile' = r(max) in `binp1' _pctile `varlist' if `touse', nq(`bin') forval i = 1/`binm1' { replace `quantile' = r(r`i') in `= `i' + 1' } // prepare data set for graph: massage tied quantiles preserve keep if `quantile' < . bysort `quantile' : gen byte `qnum' = _N by `quantile' : gen byte `qid' = _n gen `qadd' = `quantile'[_n + `qnum' - `qid' + 1] - `quantile' replace `qadd' = `qadd' * (`qid' - 1) / `qnum' replace `quantile' = `quantile' + `qadd' if `qid' > 1 gen `width' = `quantile'[_n+1] - `quantile' gen `x' = (`quantile'[_n+1] + `quantile')/2 gen `height' = `qnum' / (`bin' * `width') // vertices of bars expand 6 sort `quantile' gen byte `id' = mod(_n,6) replace `height' = 0 if (`id' <= 1 | `id' >= 4) replace `x' = `x' - 0.5 * `width' /// if `id' == 1 | `id' == 2 | `id' == 5 replace `x' = `x' + 0.5 * `width' /// if `id' == 3 | `id' == 4 | `id' == 0 } // graph _crcslbl `x' `varlist' label var `height' "density" twoway area `height' `x', bstyle(histogram) `options' end * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: RE: Histograms (was: Multiple (overlaid) Histogram)***From:*"Nick Cox" <[email protected]>

**Re: st: RE: Histograms (was: Multiple (overlaid) Histogram)***From:*Marcello Pagano <[email protected]>

**References**:**Re: st: RE: Histograms (was: Multiple (overlaid) Histogram)***From:*Marcello Pagano <[email protected]>

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