As per Shopify documentation, you cannot initialize arrays. However, you can use split filter to create one dimensional array. You cannot create associative arrays using this. However, as a workaround, use 2 arrays of same length where same index in both arrays point to related key and value as of associated array. Example code
{% assign product_type = "type-1|type-2|type-3" | split: '|' %}
{% assign product_count = "1|2|3" | split: '|' %}
{% for p_type in product_type %}
{{ p_type }}
{{ product_count[forloop.index0] }}
{% endfor %}
Expected output
Product Type Count
type-1 1
type-2 2
type-3 3
For your particular scenario explained in comments, have a look at below code and code comments. I have used checkout object for sample code. You may adjust according to your need.
// declare 2 vars to create strings - that will be converted to arrays later
{% assign product_type = "" %}
{% assign product_count = "" %}
// iterate over line_items in checkout to build product_type string
{% for line_tem in checkout.line_items %}
// if product_type exists , then skip -- unique product types
{% if product_type contains line_tem.product.type%}
{% else %}
{% assign product_type = product_type | append: '#' | append: line_tem.product.type %}
{% endif %}
{% endfor %}
// remove first extra hash and convert to array
{% assign product_type = product_type | remove_first: "#" | split: '#' %}
// iterate over unique product type array generated earlier
{% for product_type_item in product_type %}
// set product count for this product type to zero initially
{% assign total_count = 0 %}
// iterate over all lin items and +1 if same product type
{% for line_tem in checkout.line_items %}
{% if product_type_item == line_tem.product.type%}
{% assign total_count = total_count | plus: 1 %}
{% endif %}
{% endfor %}
// append count to product count string
{% assign product_count = product_count | append: '#' | append: total_count %}
{% endfor %}
// remove first extra hash and convert to array
{% assign product_count = product_count | remove_first: "#" | split: '#'%}
{{-product_type-}}
{{-product_count-}}