问题
I am trying to find two-tailed inverse of the X's t-distribution. It can be find using TINV function in Excel but I need this to achieve in SQL Sever. Please suggest me idea.
The TINV function syntax has the following arguments:
Probability : The probability associated with the two-tailed Student's t-distribution.
Deg_freedom : The number of degrees of freedom with which to characterize the distribution.
Ex:
select tinv( 0.054645, 60);
-- -----------------
-- 1.9599994129833
-- (1 row returned)
回答1:
SQL-Server does not incorporate a lot of statistical functions. tinv is not present in SQL-Server.
The only way to add a tinv function, is to use a CLR-Function.
Thus, the problem reduces itselfs to "How do I calculate tinv with the subset of C# allowed in SQL-Server ?".
If you're on .NET 4.0, you could use the chart-class in System.Web.DataVisualization.dll
e.g.
var someChart = new System.Web.UI.DataVisualization.Charting.Chart();
double res = someChart.DataManipulator.Statistics.InverseTDistribution(.05, 15);
//2.131449546
However, you probably don't want that overhead. So you'll have to rip it out of Math.NET's SourceCode (MIT/X11 License).
StudentT dist = new StudentT(0.0,1.0,7.0);
double prob = dist.CumulativeDistribution(1.8946);
Which should result in 0.95
Since you need the inverse, you'll need
StudentT.InvCDF(double location, double scale, double freedom, double p)
location: The location (μ) of the distribution.
scale: The scale (σ) of the distribution. Range: σ > 0.
freedom: The degrees of freedom (ν) for the distribution. Range: ν > 0.
p: The location at which to compute the inverse cumulative density.
[Microsoft.SqlServer.Server.SqlFunction]
public static System.Data.SqlTypes.SqlDouble TInv(double probability, int degFreedom)
{
double result = 0.00;
try
{
result = fnInverseTDistribution(degFreedom, probability);
}
catch
{
// throw; // Optionally throw/log/ignore/whatever
}
return result;
}
using DataVisualization, this goes like this:
[Microsoft.SqlServer.Server.SqlFunction]
public static System.Data.SqlTypes.SqlDouble TInv(double probability, int degFreedom)
{
double result = 0.00;
try
{
var someChart = new System.Web.UI.DataVisualization.Charting.Chart();
result = someChart.DataManipulator.Statistics.InverseTDistribution( probability, degFreedom);
}
catch
{
// throw; // Optionally throw/log/ignore/whatever
}
return result;
}
The DataVisualization trick however won't work on SQL-Server, because you'd need to add a reference to System.Web, which you can't do in SQL-Server.
Also, excel has a lot of similar functions, tinv, t.inv, T.INV.2S, etc., so be sure to choose the right one.
Edit:
Found some more information: http://numerics.mathdotnet.com/api/MathNet.Numerics/ExcelFunctions.htm#TIn
There is a special class called ExcelFunctions in Math.NET that you can actually use:
MathNet.Numerics.ExcelFunctions.TInv (1.1, 55);
You find some more information on TINV and TDIST on OpenOffice.org along with a list of functions by by category
So the solution to your problem is
[Microsoft.SqlServer.Server.SqlFunction]
public static System.Data.SqlTypes.SqlDouble TInv(double probability, int degFreedom)
{
double result = 0.00;
try
{
result = MathNet.Numerics.ExcelFunctions.TInv (probability, degFreedom);
}
catch
{
// throw; // Optionally throw/log/ignore/whatever
}
return result;
}
which is actually the same as
[Microsoft.SqlServer.Server.SqlFunction]
public static System.Data.SqlTypes.SqlDouble TInv(double probability, int degFreedom)
{
double result = 0.00;
try
{
result = -StudentT.InvCDF(0d, 1d, degFreedom, probability/2);
}
catch
{
// throw; // Optionally throw/log/ignore/whatever
}
return result;
}
So now you grab the sourcecode of Math.Net from https://github.com/mathnet/mathnet-numerics and drag and drop the contents of mathnet-numerics/src/Numerics/ (or the part thereof that you need) into your project with the CRL-Function, and finished.
When you have your CLR dll, you go into SSMS and execute:
EXEC dbo.sp_configure 'clr enabled',1 RECONFIGURE WITH
CREATE ASSEMBLY SQLServerStatistics from 'C:\SQLServerStatistics.dll' WITH PERMISSION_SET = SAFE
After that has succeeded, you still have to register the function with SQL-Server.
CREATE FUNCTION [dbo].[tinv](@prob float, @degFreedom int)
RETURNS float WITH EXECUTE AS CALLER
AS
EXTERNAL NAME [SQLServerStatistics].[Functions].[TInv]
See this article for further information.
If you want to bring the Dll onto a productive server, you'll need to create the assembly from a byte-array-string, like this:
CREATE ASSEMBLY [MyFunctions]
AUTHORIZATION [dbo]
FROM 0x4D5A90000[very long string here...];
You create the hex string from the byte array like this:
byte[] bytes = System.IO.File.ReadAllBytes(@"C:\SQLServerStatistics.dll");
"0x" + BitConverter.ToString(bytes).Replace("-", "")
I have uploaded the entire solution here on github.
Then you can run the function like this:
SELECT dbo.tinv(0.54645, 60)
==> 0.606531559343638
The Script-Generator tool automatically builds the install script for you. Looks like this:
> sp_configure 'show advanced options', 1; GO RECONFIGURE; GO
> sp_configure 'clr enabled', 1; GO RECONFIGURE; GO
>
>
> DECLARE @sql nvarchar(MAX) SET @sql = 'ALTER DATABASE ' +
> QUOTENAME(DB_NAME()) + ' SET TRUSTWORTHY ON;'
> -- PRINT @sql; EXECUTE(@sql); GO
>
>
> -- Restore sid when db restored from backup... DECLARE @Command NVARCHAR(MAX) = N'ALTER AUTHORIZATION ON DATABASE::<<DatabaseName>> TO
> [<<LoginName>>]' SELECT @Command = REPLACE ( REPLACE(@Command,
> N'<<DatabaseName>>', SD.Name) , N'<<LoginName>>' , SL.Name ) FROM
> master..sysdatabases AS SD JOIN master..syslogins AS SL ON SD.SID
> = SL.SID
>
> WHERE SD.Name = DB_NAME()
>
> -- PRINT @command EXECUTE(@command) GO
>
> IF EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[dbo].[TDist]') AND type in (N'FN', N'IF', N'TF', N'FS',
> N'FT')) DROP FUNCTION [dbo].[TDist] GO
>
> IF EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[dbo].[TInv]') AND type in (N'FN', N'IF', N'TF', N'FS',
> N'FT')) DROP FUNCTION [dbo].[TInv] GO
>
>
>
> IF EXISTS (SELECT * FROM sys.assemblies asms WHERE asms.name =
> N'SQLServerStatistics' and is_user_defined = 1) DROP ASSEMBLY
> [SQLServerStatistics] GO
>
>
> CREATE ASSEMBLY SQLServerStatistics AUTHORIZATION [dbo]
> FROM 'c:\users\administrator\documents\visual studio 2013\Projects\SqlServerStatistics\ClrCreationScriptGenerator\bin\Debug\SqlServerStatistics.dll'
> WITH PERMISSION_SET = UNSAFE GO
>
>
> CREATE FUNCTION [dbo].[TDist](@x AS float, @degFreedom AS int, @tails
> AS int)
> RETURNS float WITH EXECUTE AS CALLER AS EXTERNAL NAME [SQLServerStatistics].[SqlServerStatistics.ExcelFunctions].[TDist] GO
>
>
>
> CREATE FUNCTION [dbo].[TInv](@probability AS float, @degFreedom AS
> int)
> RETURNS float WITH EXECUTE AS CALLER AS EXTERNAL NAME [SQLServerStatistics].[SqlServerStatistics.ExcelFunctions].[TInv] GO
回答2:
You could either write your own implementation as a SQL function or use a CLR and write it in C#.
My advice would be to use a CLR and include the Accord library (I recommend this one because they still have .NET 3.5 versions which you will need for a SQL Server CLR) to implement the statistic function. I've done this for other statistic calculations in the past and it worked like a charme.
回答3:
You can use the qt function in R. Here is a code snip:
DECLARE @confinPerc float, @setCount integer
SET @confinPerc = .95
SET @setCount = 5
DROP TABLE IF EXISTS #R_RES;
CREATE TABLE #R_RES(res float);
DECLARE @sql nvarchar(100)
SET @sql =N'SELECT ' + CAST(1-@confinPerc AS NVARCHAR) + ' AS prob, ' + CAST(@setCount - 2 AS NVARCHAR) + ' AS dF;'
INSERT INTO #R_RES
EXECUTE sp_execute_external_script
@language = N'R'
,@script = N' res <- qt(1-InputDataSet$prob/2,InputDataSet$dF);
df <- data.frame(res);'
,@input_data_1 = @sql
,@output_data_1_name = N'df';
SELECT * FROM #R_RES;
来源：https://stackoverflow.com/questions/27941949/sql-server-equivalent-of-excels-tinv-function