How to find out which package manager my distrob use

#!/bin/bash
# https://stackoverflow.com/questions/19477682/bash-script-determine-vendor-and-install-system-apt-get-yum-etc
YUM_CMD=$(which yum)
APT_GET_CMD=$(which apt-get)
OTHER_CMD=$(which <other installer>)

if [[ ! -z $YUM_CMD ]]; then
    yum install $YUM_PACKAGE_NAME
 elif [[ ! -z $APT_GET_CMD ]]; then
    apt-get $DEB_PACKAGE_NAME
 elif [[ ! -z $OTHER_CMD ]]; then
    $OTHER_CMD <proper arguments>
 else
    echo "error can't install package $PACKAGE"
    exit 1;
 fi