create a new variable that is the product of lag value of another variable and its own lag value

my two input variables are age and mortality,

I want to create another variable "survival = 1" for first value of "age" like here first value of age = 65, but it can be any age

then for following ages 66, 67, 68 onwards, it should take the value from previous survival value at age 65 and mutliply with corresponding (1-mortality).

for example, my two input variables are age and mortality,

age mortality

65 0.0347029096019856

66 0.0382583912888586

67 0.0421156045159524

68 0.0463212051920102

69 0.0509158865323249

70 0.0559879627737633

my output variable is survival

age mortality survival

65 0.0347 1

66 0.0382 1*(1- 0.0347) = 0.9653

67 0.0421 0.9653 *(1-0.0382) = 0.9284

68 0.0463 0.9284*(1-0.0421) = 0.8898

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This is the code which I had written but it is giving wrong values. I do not know whether I should for-loop or is there an easy way out.

 survival = ones(size(age))

for i = 2 : length(???)
survival =  survival(i-1,:).*(1-mortality(1:end-1,:))
end 

I would appreciate your help!

Answer 1

[Rik]

survival=cumprod(1-mortality);

[susman]

Thank you for your hep. It works,

but I also need to have "1" as the first value of "survival"

and for the rest,

survival = cumprod(1-mortality) is completely fine.

[Rik]

%you can do it the long way round:
survival=cat(1+(size(mortality,1)<size(mortality,2)),1,cumprod(1-mortality(1:(end-1))));

%or pick the correct one from these:
survival=[1;cumprod(1-mortality(1:(end-1))))];
survival=[1,cumprod(1-mortality(1:(end-1))))];

[susman]

I figured that out, it should be,

survival = ones(size(age))

survival(2:end,:) = cumprod(1-mortality(1:end-1,:))