with slight modification to @Lamanus suggestion the below code might be helpful to solve your problem,
# pyspark --driver-memory 1G --executor-memory 2G --executor-cores 1 --num-executors 1
from pyspark.sql import Row
from pyspark.sql.functions import *
from pyspark.sql.window import Window
drow = Row("customer_id","month_id","m1","m2","m3","m4")
data=[drow("1001","01","10","20","10","20"),drow("1002","01","20","30","20","30"),drow("1003","01","30","40","30","40"),drow("1001","02","40","50","40","50"),drow("1002","02","50","60","50","60"),drow("1003","02","60","70","60","70"),drow("1001","03","70","80","70","80"),drow("1002","03","80","90","80","90"),drow("1003","03","90","100","90","100")]
df = spark.createDataFrame(data)
df.show()
'''
+-----------+--------+---+---+---+---+
|customer_id|month_id| m1| m2| m3| m4|
+-----------+--------+---+---+---+---+
| 1001| 01| 10| 20| 10| 20|
| 1002| 01| 20| 30| 20| 30|
| 1003| 01| 30| 40| 30| 40|
| 1001| 02| 40| 50| 40| 50|
| 1002| 02| 50| 60| 50| 60|
| 1003| 02| 60| 70| 60| 70|
| 1001| 03| 70| 80| 70| 80|
| 1002| 03| 80| 90| 80| 90|
| 1003| 03| 90|100| 90|100|
+-----------+--------+---+---+---+---+
'''
a = ["m1","m2"]
b = ["m3","m4"]
rownum_window = (Window.partitionBy("customer_id").orderBy("month_id").rangeBetween(Window.unboundedPreceding, 0))
expr = ["*",sum(col("m1")).over(rownum_window).alias("sum1"), sum(col("m2")).over(rownum_window).alias("sum2"),avg(col("m3")).over(rownum_window).alias("avg1"), avg(col("m4")).over(rownum_window).alias("avg2") ]
df.select(expr).show()
'''
+-----------+--------+---+---+---+---+-----+-----+----+----+
|customer_id|month_id| m1| m2| m3| m4| sum1| sum2|avg1|avg2|
+-----------+--------+---+---+---+---+-----+-----+----+----+
| 1003| 01| 30| 40| 30| 40| 30.0| 40.0|30.0|40.0|
| 1003| 02| 60| 70| 60| 70| 90.0|110.0|45.0|55.0|
| 1003| 03| 90|100| 90|100|180.0|210.0|60.0|70.0|
| 1002| 01| 20| 30| 20| 30| 20.0| 30.0|20.0|30.0|
| 1002| 02| 50| 60| 50| 60| 70.0| 90.0|35.0|45.0|
| 1002| 03| 80| 90| 80| 90|150.0|180.0|50.0|60.0|
| 1001| 01| 10| 20| 10| 20| 10.0| 20.0|10.0|20.0|
| 1001| 02| 40| 50| 40| 50| 50.0| 70.0|25.0|35.0|
| 1001| 03| 70| 80| 70| 80|120.0|150.0|40.0|50.0|
+-----------+--------+---+---+---+---+-----+-----+----+----+
'''