TypeScript function accept argument value from an enum

What you could do is accept a String and check that it exists in the Enum, like so:

enum Gender {Male, Female};

function validGender(c: String) {
    if(enumHasValue(Gender, c)) {
        document.write(`valid gender: ${c}`);
    } else {
        document.write(`invalid gender: ${c}`);
    }
}

function enumHasValue(e, v) {
    for (var enumMember in e) {
        if (enumMember === v) {
            return true;
        }
    }
    return false;
}

validGender("Female"); // => "valid gender: Female"
document.write("<br/>");
validGender("Alien"); // => "invalid gender: Alien"

Try this example out in the TypeScript Playground (copy and paste it in and press Run).

You can create a function to parse the gender parameter, like this:

function parseGender(value : Gender | number | string) {
  var gender;
  if (value === Number(value)) {
    gender = <Gender>value;
  }
  else if (value === String(value)) {
    if (<string>value in Gender) {
      gender = Gender[value];
    }
  }

  if (!gender) throw new TypeError("The parameter gender is incorrect");
  return gender;
}

And then you can use it inside your function:

function judgeGender(gender : Gender | number | string) {
  var g = parseGender(gender);

  // do whatever you want with g
}

You can specify which values your function can receive.

type Male = "male";
type Female = "female";

enum Gender {
    Male = Male,
    Female = Female
}

function judgeGender(gender: Gender | Male | Female) {
    //......
}

judgeGender(Gender.Male);
judgeGender("male");