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