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Rank-to-Percentile Transform on a Cross-Section of Alpha Factors
Divide-and-Conquer Sum Tree (Parallel Reduction Simulation)
Empirical Copula via Per-Column Uniform Rank Transform
Empirical Mean Excess Function for POT Threshold Selection
Empirical Upper-Tail-Dependence Coefficient from Bivariate Samples
Fit a Gumbel (GEV, ξ=0) to Block Maxima by Method of Moments
Rolling Historical Expected Shortfall (CVaR)
Fork-Join Segment Stats (Welford Pairwise Merge)
Greenwald-Khanna Streaming Quantile Summary
HDR Histogram Recorded-Value Bucket Index and Quantile Estimate
Hill Estimator for the Tail Index of a Heavy-Tailed Loss Distribution
Robust Cross-Sectional Z-Score via Median and MAD
MapReduce Group-By Count (Two-Phase Aggregation)
Merge Per-Day Bar Shards into a Sorted Timeseries
Parallel Pairwise Mean Merge with Kahan Compensation
Pareto Tail VaR via Hill-Estimator Extrapolation
Quantile Estimate from Pre-Bucketed Histogram Counts
Quintile (k-tile) Bucketing of a Cross-Sectional Factor
Cross-Sectional Rank Bucketing into Deciles with Ordinal Tie-Breaks
Spearman Rank Correlation with Average-Rank Tie Breaking
Spearman Rho and Kendall Tau-b: Dual Rank-Correlation Diagnostic for the Copula Pipeline
Realized-Volatility Jump Test (Barndorff-Nielsen and Shephard)
Rolling-Window Variance Ratio Test (Lo-MacKinlay)
Sector-Neutralize an Alpha Factor Cross-Section
Multi-Level SOR with Stale-Quote Re-Routing — Event Replay
Min-Venue-Count Smart Order Routing with Fee-Tier Crossing Penalty
SOR Across Replenishing Iceberg Venues — Event Replay
Smart-Order Routing With Bayesian Fill-Rate Priors and UCB Exploration
Survivorship-Aware Tradeable Universe on a Date
T-Digest Streaming Percentile Estimator (k_1 Scale Function)
Equal-Weight Long-Top-K / Short-Bottom-K Portfolio
Tree Reduction with (min, max) Associative Combiner