Scale parameter in probability distributions

A parameter s is called a scale parameter of a probability distribution when it follows the following property:

F(x|s,θ) = F(x/s | 1,θ)

Here, F is the cumulative distribution function (cdf) and θ represents other parameters in the distribution.

When the probability distribution function (pdf) is defined for all values, then s must follow the following property:

f_s(x) = f(x/s)/s

Here, f is pdf of the standard distribution, and  f_s is pdf of the scaled distributions.

Intuitively,  higher scale parameter means higher spread of the distribution. Standard normal distribution with different scales are shown in the following plot.

And, here is matlab code to generate the above plot.

scales = [5,2,1,0.5,0.3];
x = -10:.001:10;
for s = scales
    y = normpdf(x./s) ./ s ;
    plot(x,y);
    hold on
end
legend('scale=5', 'scale=2', 'scale=1', 'scale=0.5', 'scale=0.3')
title('Standard normal distribution with different scale parameters')

Useful Bioinformatics Links

• Samtools: 
• Install: sudo apt-get install samtools
• References
• Convert BAM file to Fastq: 
• Install picard: sudo apt-get install picard-tools
• Use SamToFastq command.
• Picard project page

Types of RNA

• mRNA: Messenger RNA. Encodes amino acids sequences.
• tRNA: Transfer RNA. Carries amino acids to ribosome during translation.
• rRNA: Ribosomal RNA. Makes up ribosomes.
• snRNA: Small Nuclear RNA (U1, U2, U4, U5, and U6).
• sRNA: Small RNA. Binds to protein or mRNA targets, and regulates gene expression.
• miRNA: Micro RNA. A family of sRNA that regulates gene expression in a sequence-specific manner.
• siRNA:  Small Interfering RNA.
• dsRNA: Double-Stranded RNA
• pre-mRNA: Precursor mRNA. Contains both exons and introns.
• mature mRNA: All introns removed.