X

Random variable X (or X
_{
t
}) that is the predicted estimate of a data point at one week(t
^{th} week)

f(x)f
_{
x
}

Probability density function (pdf) of random variable X

μ
_{
x
}

Mean value for the random variable X

\(\sigma _{x} = \sigma /{\sqrt {N_{x}}}\)

Standard deviation for the random variable X

\(\overline {x}\)

Mean value of the samples belonging to random variable X

σ

Standard deviation of the samples belonging to random variable X

v

v=N
_{
x
}−1 Degree of freedom of tdistribution

\( \bar {y} \)

\(\bar {y}=\frac {1}{n} \sum _{t=1}^{n} (y_{t}) \) : the mean for y values over n weeks

S
_{
x
}={s
_{
i
}}

where s
_{
i
} is the sample from distribution f
_{
x
}

\(N_{s_{x}} = S_{x} \)

Number of sample set S
_{
x
}

Y

Random variable Y (or Y
_{
t
}) that is the estimate of observed value at one week(t
^{th} week)

g(y)g
_{
y
}

Probability density function (pdf) of random variable Y

S
_{
y
}={s
_{
j
}}

where s
_{
j
} is the sample from distribution g
_{
x
}
