An efficient way to do this in Python is to use Show To solve
You can use the following:
The formula to the right of the sigma is represented by the lambda. The sequence we are summing is represented by the iterable. You can change these however you need. For example, if I wanted to solve:
For a sequence I
You can see the following two code lines produce the same result: For those programmers new to statistics, this section provides background on the Sigma operator, Σ. Equation 13.3. Basic Summation
The Σ operator has three parts to it. Below it is a bound variable, i and the starting value for the range, written as i=0. Above it is the ending value for the range, usually something like n. To the right is some function to execute for each value of the bound variable. In this case, a generic function, f( i). This is read as “sum f( i) for i in the range 0 to n”. One common definition of Σ uses a closed range, including the end values of 0 and n. However, since this is not a helpful definition for software, we will define Σ to use a half-open interval. It has exactly n elements, including 0 and n-1; mathematically, . Consequently, we prefer the following notation, but it is not often used. Most statistical and mathematical texts seem to use 1-based indexing, consequently some care is required when translating formulae to programming languages that use 0-based indexing. Equation 13.4. Summation with Half-Open Interval
Our two statistical algorithms have a form more like the following. In this we are applying some function, f(), to each value, xi of an array. When computing the mean, there is no function. When computing standard deviation, the function involves subtracting and multiplying. Equation 13.5. Summing Elements of an Array, x
We can transform this definition directly into a for loop that sets the bound variable to all of the values in the range, and does some processing on each value of the Example 13.2. Python Sigma Iteration sum= 0
for i in range(len(theList)):
xi= theList[i]
# fxi = processing of xi
sum += fxi
n= len(theList)
More advanced Python programmers may be aware that there are several ways to shorten this loop down to a single expression using the An Optimization. In the usual mathematical notation, an integer index, i is used. In Python it isn't necessary to use the formal integer index. Instead, an iterator can be used to visit each element of the Example 13.3. Python Sample Values by Iterator for xi in theList:
# fxi = processing of xi
sum += fxi
n= len(theList)
How do I find the Sigma?Here is the five-step process to calculate your process sigma.. Step 1: Define Your Opportunities. An opportunity is the lowest defect noticeable by a customer. ... . Step 2: Define Your Defects. ... . Step 3: Measure Your Opportunities and Defects. ... . Step 4: Calculate Your Yield. ... . Step 5: Look Up Process Sigma.. How do you find the sigma of a function?The sigma function of a positive integer n is the sum of the positive divisors of n. This is usually σ(n) using the greek letter sigma. Clearly, for primes p, σ(p)=p+1.
How do you write a summation function in Python?The sum() function is used to get the sum of all items in an iterable.. Version: ... . Syntax: sum(iterable[, start]). Parameter: ... . Return value: ... . Example: Python sum() num = [3.5, 5, 2, -5] # start parameter is not provided numSum = sum(num) print(numSum) # start = 15 numSum = sum(num, 15) print(numSum) ... . Pictorial Presentation:. |