SPC分析中用到的伽玛函数
2023/9/7 17:50:17
function [Fun_SPC_Gamma](@x float)
returns floatbegin
if @x <= 0 return 1 declare @gamma float set @gamma = 0.577215664901532860606512090
if @x <0.001 return 1.0 / (@x * (1.0 + @gamma * @x));
if @x < 12 begin
declare @y float set @y =@x
declare @n int set @n = 0
declare @arg_was_less_than_one bit if @y < 1.0 set @arg_was_less_than_one = 1 else set @arg_was_less_than_one = 0
if @arg_was_less_than_one = 1 set @y = @y + 1 else begin
set @n= cast(Floor(@y) as int) - 1 set @y =@y - @n end
declare @tbP table ( id int, const float ) insert into @tbP values(1,-1.71618513886549492533811E+0) insert into @tbP values(2,2.47656508055759199108314E+1) insert into @tbP values(3,-3.79804256470945635097577E+2) insert into @tbP values(4,6.29331155312818442661052E+2) insert into @tbP values(5,8.66966202790413211295064E+2) insert into @tbP values(6,-3.14512729688483675254357E+4) insert into @tbP values(7,-3.61444134186911729807069E+4) insert into @tbP values(8,6.64561438202405440627855E+4)
declare @tbQ table ( id int, const float ) insert into @tbQ values(1,-3.08402300119738975254353E+1) insert into @tbQ values(2,3.15350626979604161529144E+2) insert into @tbQ values(3,-1.01515636749021914166146E+3) insert into @tbQ values(4,-3.10777167157231109440444E+3) insert into @tbQ values(5,2.25381184209801510330112E+4) insert into @tbQ values(6,4.75584627752788110767815E+3) insert into @tbQ values(7,-1.34659959864969306392456E+5) insert into @tbQ values(8,-1.15132259675553483497211E+5)
declare @num float declare @den float set @num = 0 set @den = 1
declare @i int declare @z float set @z = @y - 1
set @i = 1
while @i <=8 begin
declare @p float declare @q float
select @p = const from @tbP t where id = @i
select @q = const from @tbQ t where id = @i
set @num = (@num + @p) * @z set @den = @den * @z + @q
set @i = @i + 1 end
declare @result float set @result = @num/@den + 1.0
if @arg_was_less_than_one = 1 begin set @result = @result/(@y - 1) end else begin
declare @j int set @j = 0 while @j< @n begin set @result = @result * @y set @y =@y + 1 set @j = @j + 1 end
end
return @result end
if @x > 171.624 return 1
return Exp(dbo.Fun_SPC_LogGamma(@x))
end
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