We obtain here sufficient conditions for increasing concave order and location independent more riskier order of lower record values based on stochastic comparisons of minimum order statistics. We further discuss stochastic orderings of lower record spacings. In particular, we show that increasing convex order of adjacent spacings between minimum order statistics is a sufficient condition for increasing convex order of adjacent spacings of their lower records.

中文翻译：

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较低记录和较低记录间隔的一些随机比较

基于最小阶统计的随机比较，我们在这里获得了增加凹阶和位置独立的更高风险阶的较低记录值的充分条件。我们进一步讨论了较低记录间距的随机排序。特别是，我们表明，增加最小阶统计量之间相邻间距的凸阶是增加其较低记录的相邻间距凸阶的充分条件。