LMC 价格收敛指数
一个稳健的离散度指标,每周衡量AI模型市场在四个质量层级中价格分布的紧密程度。它使用log10美元空间中的双权重中方差(biweight midvariance),并通过BCa自助法报告80%置信区间。
前10最强模型的中位输出价格在 $10.3 与 $4.80 之间下降,6 周内幅度 53.5%。
复合周降幅 12.0%。同期PCI从 0.969 收敛到 0.773(幅度 20.2%)。
日用层中位价从 $0.78 升至 $0.93(幅度 19.8%)。
日用层包括所有付费的编码模型,输出价格 < $50/M。这是云端买家实际感受到的价格层。当前样本量 n=276。
PCI biweight midvariance
same slugs throughout
paid coding, < $50/M out
稳健 PCI = log10 价格的双权重中方差
| 周 | 前沿 PCI | CI80 | 前沿中位价 |
|---|---|---|---|
| 02-16 | 0.969 | 0.863-1.159 | $10.3 |
| 02-23 | 0.504 | 0.063-1.049 | $9.66 |
| 03-02 | 0.957 | 0.843-1.135 | $9.66 |
| 03-09 | 0.824 | 0.609-1.041 | $7.56 |
| 03-16 | 0.773 | 0.592-1.028 | $4.80 |
| 03-23 | 0.773 | 0.590-1.034 | $4.80 |
| 03-30 | 0.773 | 0.578-1.005 | $4.80 |
留一服务商法(LOPO):将该服务商的所有模型从前沿层中剔除后,方差下降的份额。负值意味着该服务商的价格实际上拉低了方差。
形式定义、层级定义、为什么使用对数分散度、估计量选择、worked example、变更日志、参考文献。
阅读所有四个层级的全部时间序列,包括稳健PCI、stdev、IQR、中位数、80%置信区间和趋势斜率。
/api/pci/seriesPCI measures how tightly priced a quality tier of the AI model market is around its own median, in log10 dollar space. The headline value is the biweight midvariance of log blended prices for the 10 models in the rolling frontier tier. A PCI near 0 means prices are clustered into a narrow band; a PCI near 1 means prices span a full order of magnitude. We work in log space because token pricing varies across roughly four orders of magnitude (sub-cent per million to several hundred dollars per million), which makes any linear measure useless.
Sample standard deviation has 100 percent efficiency at the Gaussian but 0 percent breakdown - one extreme outlier completely controls the value. With only 10 models in the frontier tier, that is a fatal property for a metric we want to publish. Biweight midvariance retains 87 percent Gaussian efficiency while tolerating up to 50 percent contamination, so a single mispriced or experimentally-priced flagship cannot move the headline. We still publish the sample stdev alongside as the raw measure for readers who prefer the textbook formula.
The trend slope is estimated by OLS regression of log(PCI) on the week index, with an 80 percent CI from a moving block bootstrap. With only 7 weekly observations the CI on the slope is necessarily wide, and that is the correct, honest answer. We refuse to publish a tighter CI than the data supports, and we will not publish any long-run floor estimate until we have at least 20 weekly observations. The current slope is -0.0011 per week with an 80 percent CI of (-0.0417, +0.0414).
Rolling top-10 uses whichever 10 models hold the top spots on the live leaderboard each week, so the membership changes whenever a new flagship launches or an old one is overtaken. Composition-fixed uses the same 10 slugs across every week (the latest week's top 10), with no backfill - if a slug did not exist in an early week we simply drop it from that week's sample, and we report the smaller n. The two series tell you different things. Rolling answers "what does the current frontier cost". Composition-fixed answers "how have these specific 10 models repriced over time". The gap between them is the composition effect.
Two reasons. First, the long tail of premium endpoints (image generation video, reasoning specialist tiers above $500/M) is so far above the main commodity market in price that including them turns the dispersion into a measure of "is the long tail still long" rather than "is the commodity market converging". Second, those endpoints are typically priced as launch experiments and reprice on quarterly or annual cycles, contributing pure noise to a weekly metric. The commodity tier on this page additionally caps at $50/M to track the cloud-buyer surface specifically.
Mostly no, by construction. Biweight midvariance downweights any single observation more than three or four MADs away from the median by zero, so a single anomalous price has bounded influence on the headline. The per-provider variance contribution table on this page shows leave-one-provider-out shares so you can see directly which provider currently moves the metric the most. In the latest week, the largest single contributor is xAI at 18 percent of variance.