<doc-data|<doc-title|bkshuf: A Shuf-Like Utility with Pre-Image Resistance
and Relative Order Preservation for Random Sampling of Long
Lists>|<doc-author|<author-data|<author-name|Steven Baltakatei
- Sandoval>>>|<doc-date|2023-02-14T13:48+00>|<doc-misc|CC BY-SA 4.0>>
+ Sandoval>>>|<doc-date|2023-02-14T13:56+00>|<doc-misc|CC BY-SA 4.0>>
<section|Summary>
size trends towards <math|s>.
<\eqnarray*>
- <tformat|<table|<row|<cell|p<rsub|<text|seq>>>|<cell|=>|<cell|<around*|(|1-p<rsub|<text|jump>>|)>>>|<row|<cell|p<rsub|<text|jump>>>|<cell|=>|<cell|1-p<rsub|<text|seq>>>>|<row|<cell|s>|<cell|=>|<cell|<frac|1|p<rsub|<text|jump>>>=<frac|1|1-p<rsub|<text|seq>>><eq-number>>>|<row|<cell|s>|<cell|=>|<cell|<frac|1|1-p<rsub|<text|seq>>>>>|<row|<cell|1-p<rsub|<text|seq>>>|<cell|=>|<cell|<frac|1|s>>>|<row|<cell|p<rsub|<text|seq>>-1>|<cell|=>|<cell|<frac|-1|s>>>|<row|<cell|p<rsub|<text|seq>>>|<cell|=>|<cell|1-<frac|1|s<around*|(|l<rsub|<text|in>>|)>><eq-number><inactive|<label|eq
- pseq-from-s-lin>>>>|<row|<cell|p<rsub|<text|jump>>>|<cell|=>|<cell|<frac|1|s<around*|(|l<rsub|<text|in>>|)>><eq-number><inactive|<label|eq
- pjump-from-s-lin>>>>|<row|<cell|>|<cell|>|<cell|>>|<row|<cell|p<rsub|<text|seq>><around*|(|l<rsub|<text|in>>|)>>|<cell|=>|<cell|1-<around*|[|<around*|(|<frac|s<around*|(|l<rsub|<text|in>,0>|)>-1|<around*|[|ln
- <around*|(|l<rsub|<text|in>,0>|)>|]><rsup|2>>|)>\<cdot\><around*|[|<text|ln><around*|(|l<rsub|<text|in>>|)>|]><rsup|2>+1|]><rsup|-1><eq-number><inactive|<label|eq
- pseq-from-s-lin-exp>>>>>>
+ <tformat|<table|<row|<cell|p<rsub|<text|seq>>>|<cell|=>|<cell|<around*|(|1-p<rsub|<text|jump>>|)>>>|<row|<cell|p<rsub|<text|jump>>>|<cell|=>|<cell|1-p<rsub|<text|seq>>>>|<row|<cell|s>|<cell|=>|<cell|<frac|1|p<rsub|<text|jump>>>=<frac|1|1-p<rsub|<text|seq>>><eq-number>>>|<row|<cell|s>|<cell|=>|<cell|<frac|1|1-p<rsub|<text|seq>>>>>|<row|<cell|1-p<rsub|<text|seq>>>|<cell|=>|<cell|<frac|1|s>>>|<row|<cell|p<rsub|<text|seq>>-1>|<cell|=>|<cell|<frac|-1|s>>>|<row|<cell|p<rsub|<text|seq>>>|<cell|=>|<cell|1-<frac|1|s<around*|(|l<rsub|<text|in>>|)>><eq-number><label|eq
+ pseq-from-s-lin>>>|<row|<cell|p<rsub|<text|jump>>>|<cell|=>|<cell|<frac|1|s<around*|(|l<rsub|<text|in>>|)>><eq-number><label|eq
+ pjump-from-s-lin>>>|<row|<cell|>|<cell|>|<cell|>>|<row|<cell|p<rsub|<text|seq>><around*|(|l<rsub|<text|in>>|)>>|<cell|=>|<cell|1-<around*|[|<around*|(|<frac|s<around*|(|l<rsub|<text|in>,0>|)>-1|<around*|[|ln
+ <around*|(|l<rsub|<text|in>,0>|)>|]><rsup|2>>|)>\<cdot\><around*|[|<text|ln><around*|(|l<rsub|<text|in>>|)>|]><rsup|2>+1|]><rsup|-1><eq-number><label|eq
+ pseq-from-s-lin-exp>>>>>
</eqnarray*>
<subsubsection|Jump from random variate of inverse gaussian distribution>
<\references>
<\collection>
<associate|auto-1|<tuple|1|1|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
- <associate|auto-10|<tuple|3.3.3|4|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
+ <associate|auto-10|<tuple|3.3.3|5|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|auto-11|<tuple|3.3.4|5|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|auto-12|<tuple|4|5|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|auto-13|<tuple|1|5|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|auto-14|<tuple|1|?|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|auto-2|<tuple|2|1|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
- <associate|auto-3|<tuple|3|1|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
- <associate|auto-4|<tuple|3.1|1|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
+ <associate|auto-3|<tuple|3|2|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
+ <associate|auto-4|<tuple|3.1|2|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|auto-5|<tuple|3.2|2|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|auto-6|<tuple|3.3|2|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|auto-7|<tuple|3.3.1|2|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|eq gsize-lin|<tuple|6|4|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|eq gsize-model|<tuple|3|3|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|eq gsize-param-rel|<tuple|4|3|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
+ <associate|eq pjump-from-s-lin|<tuple|11|?|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
+ <associate|eq pseq-from-s-lin|<tuple|10|?|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
+ <associate|eq pseq-from-s-lin-exp|<tuple|12|?|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|eq rel-x-lin|<tuple|1|3|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|eq rel-x0-lin0|<tuple|2|3|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>
<associate|fig ex-plot-s|<tuple|1|3|../../../../../wr/20230213..bkshuf_draft/src/doc.tm>>