Get count of custom post type created by current user

I’m trying to get the count of published posts in a custom post type for the current user (to display on a profile page).

I found this here on the forums:

<?php
global $wp_query;
$curauth = $wp_query->get_queried_object();
$post_count = $wpdb->get_var("SELECT COUNT(*) FROM $wpdb->posts WHERE post_author="" . $curauth->ID . "" AND post_type="user_video" AND post_status="publish"");
?>

But, it’s just giving me a big fat ZERO even though there are definitely published posts of that type. What am I doing wrong and is there a better way to do this?

I’m posting a new answer because I found this thread while searching for the same thing and the solutions here weren’t optimal.

The post_type argument can be a string or an array of post types.

function custom_count_posts_by_author($user_id, $post_type = array('post', 'page', 'custom_post_type'))
{
    $args = array(
        'post_type'      => $post_type,
        'author'         => $user_id,
        'post_status'    => 'publish',
        'posts_per_page' => -1
    );

    $query = new WP_Query($args);

    return $query->found_posts;
}