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Kotlin Notebook
Probieren Sie diesen Leitfaden als Kotlin Notebook mit Kandy-Visualisierungen aus — führen Sie die Zellen aus, um Diagramme zu sehen und die Daten interaktiv zu erkunden.
Jede Verteilung kodiert Annahmen darüber, welche Werte möglich sind und wie wahrscheinlich sie auftreten. Dieser Leitfaden gruppiert Verteilungen nach der Art der modellierten Daten und zeigt, wie Sie die Anpassungsgüte überprüfen.
// API response times — often right-skewed with a long tailval responseTime = LogNormalDistribution(mu = 4.5, sigma = 0.8)responseTime.mean // expected average in msresponseTime.quantile(0.95) // P95 latencyresponseTime.quantile(0.99) // P99 latencyresponseTime.cdf(200.0) // probability of responding under 200ms
// Time between server errors — memoryless waiting processval timeBetweenErrors = ExponentialDistribution(rate = 0.5)timeBetweenErrors.mean // average time between errorstimeBetweenErrors.sf(10.0) // probability of waiting longer than 10 unitstimeBetweenErrors.quantile(0.5) // median waiting time
// Hardware component lifetime — models wear-out (shape > 1) or burn-in (shape < 1)val componentLifetime = WeibullDistribution(shape = 2.0, scale = 5000.0)componentLifetime.quantile(0.1) // 10% of components fail before this timecomponentLifetime.cdf(3000.0) // probability of failure before 3000 hourscomponentLifetime.sf(4000.0) // probability of surviving past 4000 hours
// Errors per hour on a production serverval errorsPerHour = PoissonDistribution(rate = 3.2)errorsPerHour.pmf(0) // probability of zero errorserrorsPerHour.cdf(5) // probability of at most 5 errorserrorsPerHour.quantileInt(0.99) // error count exceeded only 1% of the time
// Conversions out of 1000 page views with 3.5% conversion rateval conversions = BinomialDistribution(trials = 1000, probability = 0.035)conversions.mean // expected number of conversionsconversions.pmf(40) // probability of exactly 40 conversionsconversions.sf(50) // probability of more than 50 conversions
// Support tickets until 5th resolution (variance > mean)val tickets = NegativeBinomialDistribution(successes = 5, probability = 0.1)tickets.mean // expected ticket counttickets.variance // larger than mean — overdispersion
// User session duration in minutes (roughly symmetric)val sessionDuration = NormalDistribution(mu = 12.5, sigma = 3.2)sessionDuration.cdf(15.0) // probability of session under 15 minsessionDuration.quantile(0.95) // 95th percentile// Small-sample estimate — heavier tails give more conservative intervalsval smallSampleEstimate = StudentTDistribution(degreesOfFreedom = 8.0)smallSampleEstimate.quantile(0.975) // critical value for 95% CI
Vergleichen Sie nach der Wahl einer Verteilung diese mit den beobachteten Daten mithilfe des Kolmogorov-Smirnov-Tests.
val processingTimesMs = doubleArrayOf( 45.2, 51.8, 48.1, 52.3, 47.6, 49.9, 53.1, 46.5, 50.7, 48.8, 51.2, 47.3, 49.1, 52.8, 46.9, 50.3, 48.5, 51.6, 47.8, 49.4)// Fit a Normal from sample statisticsval fitted = NormalDistribution( mu = processingTimesMs.mean(), sigma = processingTimesMs.standardDeviation())val ks = kolmogorovSmirnovTest(processingTimesMs, fitted)ks.statistic // KS statistic — smaller means better fitks.pValue // high p-value means data does not contradict the distribution
Ein nicht-signifikanter KS-Test beweist nicht, dass die Verteilung korrekt ist — er bedeutet lediglich, dass die Daten dieser Wahl nicht stark widersprechen.
