Regression methods for the appearances of extremes in climate data

For any given city, on any calendar day, there will be record high and low temperatures. Which record occurred earlier? If there is a trend towards warming then, intuitively, there should be a preponderance of record highs occurring more recently than the record lows for each of the 365 calendar days. We are interested in modeling the joint distribution of appearances of the extremes but not these values themselves. We develop a bivariate discrete distribution modeling the joint indices of maximum and minimum in a sequence of independent random variables sampled from different distributions. We assume these distributions share a proportional hazard rate and develop regression methods for these paired values. This approach has reasonable power to detect a small mean change over a decade. Using readily available public data, we examine the daily calendar extreme values of five US cities for the decade 2011–2020. We develop linear regression models for these data, describe models to account for calendar‐date dependence, and use diagnostic measures to detect remarkable observations.