King said his son Andy King died unexpectedly of a heart attack on July 28.
His daughter, Chaia King, died on August 20 shortly after she was diagnosed with lung cancer.
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He said both of his children were good and kind souls who will be greatly missed.
"Losing them feels so out of order. No parent should have to bury a child," King said in a statement posted to social media.
He thanked the public for their support but asked for time and privacy to heal.
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