"As much as he influenced and touched so many millions around the world, his influence at home was immeasurable," his daughter Kerri Kasem tells PEOPLE. "He taught us to be selfless, humble and passionate about doing the right thing no matter how difficult or long the road may be. I am who I am because of my dad."
Kerri, who fought an acrimonious battle with her stepmother in the final months of her father's life, as they argued over his care and final wishes, says she has created a foundation in her father's memory, in the hope of helping others avoid the emotional struggle she faced as her father's health declined.
"My dad always said that helping others is the most rewarding thing you can do in life," Kerri says. "I created the Kasem Cares Foundation to help enact legislation that would give visitation rights to adult children with an ailing parent."
She says that the bill is currently being considered by the California senate. Kerri was appointed conservator for her father in the final days of his life but her stepmother, Jean, who is the executor of Casey's will, is handling the arrangements for a private funeral for family and close friends later this week. His remains have been turned over to her, TMZ reports.
While they continue to grieve, his three older children are looking back at their father's life and career, which also included voice-over work, TV and movie roles and supporting a lot of charitable causes.
"The reason our dad was able to touch so many hearts around the world on Sunday mornings [with American Top 40] was because every word he spoke was 100 percent genuine," his son, Mike, tells PEOPLE. "I realized that when I saw him cry while reading a long-distance dedication."
"Education was very important to my dad," adds daughter Julie. "Throughout college and grad school he was cheerleader and a steady wind at my back. He would call me every day to ask about my exams and encouraged me to work hard."
"My dad always said, 'No matter what you do, strive to be the best. If you are going to be a chimney sweep, be the best damn chimney sweep in the world.' "
Reporting by PATRICK GOMEZ